Zhang, Qi; Pan, Xinghong [Pan, X.; Zhang, Q.] A review of results on axially symmetric Navier-Stokes equations, with addendum by X. Pan and Q. Zhang. (English) Zbl 07568029 Anal. Theory Appl. 38, No. 3, 243-296 (2022). MSC: 35Q30 76N10 PDF BibTeX XML Cite \textit{Q. Zhang} and \textit{X. Pan}, Anal. Theory Appl. 38, No. 3, 243--296 (2022; Zbl 07568029) Full Text: DOI arXiv OpenURL
Wang, Yanqing; Jiu, Quansen; Wei, Wei Leray’s backward self-similar solutions to the 3D Navier-Stokes equations in Morrey spaces. (English) Zbl 1492.35188 SIAM J. Math. Anal. 54, No. 3, 2768-2791 (2022). Reviewer: Piotr Biler (Wrocław) MSC: 35Q30 76D05 35B65 35D30 35C06 35A01 PDF BibTeX XML Cite \textit{Y. Wang} et al., SIAM J. Math. Anal. 54, No. 3, 2768--2791 (2022; Zbl 1492.35188) Full Text: DOI arXiv OpenURL
Bedrossian, Jacob; Gualdani, Maria Pia; Snelson, Stanley Non-existence of some approximately self-similar singularities for the Landau, Vlasov-Poisson-Landau, and Boltzmann equations. (English) Zbl 1484.35079 Trans. Am. Math. Soc. 375, No. 3, 2187-2216 (2022). MSC: 35B44 35C06 35Q49 35Q83 35Q20 PDF BibTeX XML Cite \textit{J. Bedrossian} et al., Trans. Am. Math. Soc. 375, No. 3, 2187--2216 (2022; Zbl 1484.35079) Full Text: DOI arXiv OpenURL
Albritton, Dallas; Bradshaw, Zachary Non-decaying solutions to the critical surface quasi-geostrophic equations with symmetries. (English) Zbl 1481.35305 Trans. Am. Math. Soc. 375, No. 1, 587-625 (2022). MSC: 35Q30 35Q86 76D05 76U05 86A05 35C06 35B40 35B32 35A01 PDF BibTeX XML Cite \textit{D. Albritton} and \textit{Z. Bradshaw}, Trans. Am. Math. Soc. 375, No. 1, 587--625 (2022; Zbl 1481.35305) Full Text: DOI arXiv OpenURL
Bradshaw, Zachary; Tsai, Tai-Peng On the local pressure expansion for the Navier-Stokes equations. (English) Zbl 07425737 J. Math. Fluid Mech. 24, No. 1, Paper No. 3, 32 p. (2022). MSC: 76-XX PDF BibTeX XML Cite \textit{Z. Bradshaw} and \textit{T.-P. Tsai}, J. Math. Fluid Mech. 24, No. 1, Paper No. 3, 32 p. (2022; Zbl 07425737) Full Text: DOI arXiv OpenURL
Farwig, Reinhard From Jean Leray to the millennium problem: the Navier-Stokes equations. (English) Zbl 1492.35002 J. Evol. Equ. 21, No. 3, 3243-3263 (2021); correction ibid. 21, No. 3, 3265-3266 (2021). Reviewer: Evan Miller (Hamilton) MSC: 35-02 35Q30 76D05 35B65 35B44 PDF BibTeX XML Cite \textit{R. Farwig}, J. Evol. Equ. 21, No. 3, 3243--3263 (2021; Zbl 1492.35002) Full Text: DOI OpenURL
Elgindi, Tarek Finite-time singularity formation for \(C^{1,\alpha}\) solutions to the incompressible Euler equations on \(\mathbb{R}^3\). (English) Zbl 1492.35199 Ann. Math. (2) 194, No. 3, 647-727 (2021). Reviewer: Ming Mei (Montreal) MSC: 35Q31 35B40 35B35 35B45 35B20 PDF BibTeX XML Cite \textit{T. Elgindi}, Ann. Math. (2) 194, No. 3, 647--727 (2021; Zbl 1492.35199) Full Text: DOI arXiv OpenURL
Lai, Baishun; Miao, Changxing; Zheng, Xiaoxin Global regularity of weak solutions to the generalized Leray equations and its applications. (English) Zbl 1479.35622 Trans. Am. Math. Soc. 374, No. 10, 7449-7497 (2021). MSC: 35Q30 35B40 76D05 76D07 35B65 35D30 35C06 26A33 35R11 PDF BibTeX XML Cite \textit{B. Lai} et al., Trans. Am. Math. Soc. 374, No. 10, 7449--7497 (2021; Zbl 1479.35622) Full Text: DOI arXiv OpenURL
Du, Dapeng On some model equations of Euler and Navier-Stokes equations. (English) Zbl 1475.35230 Chin. Ann. Math., Ser. B 42, No. 2, 281-290 (2021). MSC: 35Q30 35Q31 76D05 76F02 76D03 44A15 42A38 35A01 PDF BibTeX XML Cite \textit{D. Du}, Chin. Ann. Math., Ser. B 42, No. 2, 281--290 (2021; Zbl 1475.35230) Full Text: DOI arXiv OpenURL
Barker, Tobias; Prange, Christophe Quantitative regularity for the Navier-Stokes equations via spatial concentration. (English) Zbl 1472.35266 Commun. Math. Phys. 385, No. 2, 717-792 (2021). Reviewer: Ilya A. Chernov (Petrozavodsk) MSC: 35Q30 76D05 35B45 35B44 35B65 PDF BibTeX XML Cite \textit{T. Barker} and \textit{C. Prange}, Commun. Math. Phys. 385, No. 2, 717--792 (2021; Zbl 1472.35266) Full Text: DOI arXiv OpenURL
Germain, Pierre; Iwabuchi, Tsukasa; Léger, Tristan On self-similar solutions to degenerate compressible Navier-Stokes equations. (English) Zbl 1466.76040 Commun. Math. Phys. 381, No. 3, 1001-1030 (2021). Reviewer: Ilya A. Chernov (Petrozavodsk) MSC: 76N10 76N06 35Q30 76M55 80A19 PDF BibTeX XML Cite \textit{P. Germain} et al., Commun. Math. Phys. 381, No. 3, 1001--1030 (2021; Zbl 1466.76040) Full Text: DOI arXiv OpenURL
Germain, Pierre; Iwabuchi, Tsukasa; Léger, Tristan Backward self-similar solutions for compressible Navier-Stokes equations. (English) Zbl 1460.35256 Nonlinearity 34, No. 2, 868-893 (2021). MSC: 35Q30 35C06 76N10 35B44 35B06 35A01 PDF BibTeX XML Cite \textit{P. Germain} et al., Nonlinearity 34, No. 2, 868--893 (2021; Zbl 1460.35256) Full Text: DOI arXiv OpenURL
Wang, Yanqing; Wu, Gang; Zhou, Daoguo \(\varepsilon\)-regularity criteria in anisotropic Lebesgue spaces and Leray’s self-similar solutions to the 3D Navier-Stokes equations. (English) Zbl 1466.35290 Z. Angew. Math. Phys. 71, No. 5, Paper No. 164, 19 p. (2020). Reviewer: Gelu Paşa (Bucureşti) MSC: 35Q30 35B65 35D30 76D05 35C06 PDF BibTeX XML Cite \textit{Y. Wang} et al., Z. Angew. Math. Phys. 71, No. 5, Paper No. 164, 19 p. (2020; Zbl 1466.35290) Full Text: DOI arXiv OpenURL
Elgindi, Tarek M.; Jeong, In-Jee Finite-time singularity formation for strong solutions to the Boussinesq system. (English) Zbl 1462.35287 Ann. PDE 6, No. 1, Paper No. 5, 50 p. (2020). MSC: 35Q35 35Q31 35D35 35A01 35A02 35B44 76B47 PDF BibTeX XML Cite \textit{T. M. Elgindi} and \textit{I.-J. Jeong}, Ann. PDE 6, No. 1, Paper No. 5, 50 p. (2020; Zbl 1462.35287) Full Text: DOI arXiv OpenURL
Pan, Xinghong; Li, Zijin Liouville theorem of axially symmetric Navier-Stokes equations with growing velocity at infinity. (English) Zbl 1451.35040 Nonlinear Anal., Real World Appl. 56, Article ID 103159, 8 p. (2020). MSC: 35B53 35Q30 PDF BibTeX XML Cite \textit{X. Pan} and \textit{Z. Li}, Nonlinear Anal., Real World Appl. 56, Article ID 103159, 8 p. (2020; Zbl 1451.35040) Full Text: DOI arXiv OpenURL
Barker, Tobias; Prange, Christophe Scale-invariant estimates and vorticity alignment for Navier-Stokes in the half-space with no-slip boundary conditions. (English) Zbl 1434.35042 Arch. Ration. Mech. Anal. 235, No. 2, 881-926 (2020). MSC: 35Q30 35B65 35B44 76D05 76D10 PDF BibTeX XML Cite \textit{T. Barker} and \textit{C. Prange}, Arch. Ration. Mech. Anal. 235, No. 2, 881--926 (2020; Zbl 1434.35042) Full Text: DOI arXiv OpenURL
Elgindi, Tarek M.; Jeong, In-Jee Finite-time singularity formation for strong solutions to the axi-symmetric \(3D\) Euler equations. (English) Zbl 1436.35055 Ann. PDE 5, No. 2, Paper No. 16, 51 p. (2019). MSC: 35B44 35A20 35Q31 35B07 PDF BibTeX XML Cite \textit{T. M. Elgindi} and \textit{I.-J. Jeong}, Ann. PDE 5, No. 2, Paper No. 16, 51 p. (2019; Zbl 1436.35055) Full Text: DOI arXiv OpenURL
Bradshaw, Zachary; Tsai, Tai-Peng Discretely self-similar solutions to the Navier-Stokes equations with data in \(L_{\text{loc}}^2\) satisfying the local energy inequality. (English) Zbl 1431.35100 Anal. PDE 12, No. 8, 1943-1962 (2019). MSC: 35Q30 76D05 35C06 35D30 PDF BibTeX XML Cite \textit{Z. Bradshaw} and \textit{T.-P. Tsai}, Anal. PDE 12, No. 8, 1943--1962 (2019; Zbl 1431.35100) Full Text: DOI arXiv OpenURL
Maekawa, Yasunori; Miura, Hideyuki; Prange, Christophe On stability of blow-up solutions of the Burgers vortex type for the Navier-Stokes equations with a linear strain. (English) Zbl 1431.35137 J. Math. Fluid Mech. 21, No. 4, Paper No. 46, 23 p. (2019). MSC: 35Q35 35A01 35B35 35B40 35B44 35Q30 76D05 76E30 76D17 76D03 PDF BibTeX XML Cite \textit{Y. Maekawa} et al., J. Math. Fluid Mech. 21, No. 4, Paper No. 46, 23 p. (2019; Zbl 1431.35137) Full Text: DOI arXiv OpenURL
Zhang, Jingjing; Zhang, Ting Global existence of discretely self-similar solutions to the generalized MHD system in Besov space. (English) Zbl 1448.76201 J. Math. Phys. 60, No. 8, 081515, 18 p. (2019). MSC: 76W05 35C06 35Q35 35A01 35R11 PDF BibTeX XML Cite \textit{J. Zhang} and \textit{T. Zhang}, J. Math. Phys. 60, No. 8, 081515, 18 p. (2019; Zbl 1448.76201) Full Text: DOI OpenURL
Albritton, Dallas; Barker, Tobias On local type I singularities of the Navier – Stokes equations and Liouville theorems. (English) Zbl 1448.35359 J. Math. Fluid Mech. 21, No. 3, Paper No. 43, 11 p. (2019). MSC: 35Q30 35B53 35A21 35D30 PDF BibTeX XML Cite \textit{D. Albritton} and \textit{T. Barker}, J. Math. Fluid Mech. 21, No. 3, Paper No. 43, 11 p. (2019; Zbl 1448.35359) Full Text: DOI arXiv OpenURL
Lai, Chen-Chih Forward discretely self-similar solutions of the MHD equations and the viscoelastic Navier-Stokes equations with damping. (English) Zbl 1418.76012 J. Math. Fluid Mech. 21, No. 3, Paper No. 38, 28 p. (2019). MSC: 76A10 76W05 76D03 PDF BibTeX XML Cite \textit{C.-C. Lai}, J. Math. Fluid Mech. 21, No. 3, Paper No. 38, 28 p. (2019; Zbl 1418.76012) Full Text: DOI arXiv OpenURL
Lai, Baishun; Miao, Changxing; Zheng, Xiaoxin Forward self-similar solutions of the fractional Navier-Stokes equations. (English) Zbl 1420.35192 Adv. Math. 352, 981-1043 (2019). MSC: 35Q30 35B40 76D05 35R11 35B44 35C06 35B65 PDF BibTeX XML Cite \textit{B. Lai} et al., Adv. Math. 352, 981--1043 (2019; Zbl 1420.35192) Full Text: DOI arXiv OpenURL
Cao, Xiangdi; Chen, Qionglei; Lai, Baishun Properties of the linear non-local Stokes operator and its application. (English) Zbl 1426.35176 Nonlinearity 32, No. 7, 2633-2666 (2019). Reviewer: Jürgen Socolowsky (Brandenburg an der Havel) MSC: 35Q30 35B65 35B40 76D03 76D05 35R11 PDF BibTeX XML Cite \textit{X. Cao} et al., Nonlinearity 32, No. 7, 2633--2666 (2019; Zbl 1426.35176) Full Text: DOI OpenURL
Albritton, Dallas; Barker, Tobias Global weak Besov solutions of the Navier-Stokes equations and applications. (English) Zbl 1412.35213 Arch. Ration. Mech. Anal. 232, No. 1, 197-263 (2019). MSC: 35Q30 35D30 35B35 35B44 35C06 35B65 76D05 PDF BibTeX XML Cite \textit{D. Albritton} and \textit{T. Barker}, Arch. Ration. Mech. Anal. 232, No. 1, 197--263 (2019; Zbl 1412.35213) Full Text: DOI arXiv OpenURL
Liu, Xian-gao; Zhang, Xiaotao Liouville theorem for MHD system and its applications. (English) Zbl 1397.35214 Commun. Pure Appl. Anal. 17, No. 6, 2329-2350 (2018). MSC: 35Q35 76W05 35B65 35D30 35B07 PDF BibTeX XML Cite \textit{X.-g. Liu} and \textit{X. Zhang}, Commun. Pure Appl. Anal. 17, No. 6, 2329--2350 (2018; Zbl 1397.35214) Full Text: DOI OpenURL
Bradshaw, Zachary; Tsai, Tai-Peng Discretely self-similar solutions to the Navier-Stokes equations with Besov space data. (English) Zbl 1394.35316 Arch. Ration. Mech. Anal. 229, No. 1, 53-77 (2018). MSC: 35Q30 76D05 35C06 35D30 35B10 PDF BibTeX XML Cite \textit{Z. Bradshaw} and \textit{T.-P. Tsai}, Arch. Ration. Mech. Anal. 229, No. 1, 53--77 (2018; Zbl 1394.35316) Full Text: DOI arXiv OpenURL
Guevara, Cristi; Phuc, Nguyen Cong Leray’s self-similar solutions to the Navier-Stokes equations with profiles in Marcinkiewicz and Morrey spaces. (English) Zbl 1391.35314 SIAM J. Math. Anal. 50, No. 1, 541-556 (2018). Reviewer: Gheorghe Moroşanu (Budapest) MSC: 35Q30 35C06 PDF BibTeX XML Cite \textit{C. Guevara} and \textit{N. C. Phuc}, SIAM J. Math. Anal. 50, No. 1, 541--556 (2018; Zbl 1391.35314) Full Text: DOI arXiv OpenURL
Shi, Zuoshunhua Self-similar solutions of stationary Navier-Stokes equations. (English) Zbl 1378.35229 J. Differ. Equations 264, No. 3, 1550-1580 (2018). MSC: 35Q30 76D03 35B40 35C06 35B06 PDF BibTeX XML Cite \textit{Z. Shi}, J. Differ. Equations 264, No. 3, 1550--1580 (2018; Zbl 1378.35229) Full Text: DOI OpenURL
Farwig, Reinhard Jean Leray: Sur le mouvement d’un liquide visqueux emplissant l’espace. Acta Math. 63 (1934), 193–248. (English) Zbl 1373.76004 Jahresber. Dtsch. Math.-Ver. 119, No. 4, 249-272 (2017). MSC: 76-03 76D05 01A70 PDF BibTeX XML Cite \textit{R. Farwig}, Jahresber. Dtsch. Math.-Ver. 119, No. 4, 249--272 (2017; Zbl 1373.76004) Full Text: DOI OpenURL
Chae, Dongho; Wolf, Jörg On the Liouville type theorems for self-similar solutions to the Navier-Stokes equations. (English) Zbl 1367.35104 Arch. Ration. Mech. Anal. 225, No. 1, 549-572 (2017). MSC: 35Q30 76D05 35C06 PDF BibTeX XML Cite \textit{D. Chae} and \textit{J. Wolf}, Arch. Ration. Mech. Anal. 225, No. 1, 549--572 (2017; Zbl 1367.35104) Full Text: DOI arXiv OpenURL
Miao, Changxing; Wang, Yanqing Regularity conditions for suitable weak solutions of the Navier-Stokes system from its rotation form. (English) Zbl 1364.35243 Pac. J. Math. 288, No. 1, 189-215 (2017). MSC: 35Q30 35B65 35D30 76U05 76D05 PDF BibTeX XML Cite \textit{C. Miao} and \textit{Y. Wang}, Pac. J. Math. 288, No. 1, 189--215 (2017; Zbl 1364.35243) Full Text: DOI OpenURL
Bradshaw, Zachary; Tsai, Tai-Peng Forward discretely self-similar solutions of the Navier-Stokes equations. II. (English) Zbl 1368.35204 Ann. Henri Poincaré 18, No. 3, 1095-1119 (2017). Reviewer: Gelu Paşa (Bucureşti) MSC: 35Q30 76D05 35C06 PDF BibTeX XML Cite \textit{Z. Bradshaw} and \textit{T.-P. Tsai}, Ann. Henri Poincaré 18, No. 3, 1095--1119 (2017; Zbl 1368.35204) Full Text: DOI arXiv OpenURL
Ohkitani, Koji Near-invariance under dynamic scaling for Navier-Stokes equations in critical spaces: a probabilistic approach to regularity problems. (English) Zbl 1357.76015 J. Phys. A, Math. Theor. 50, No. 4, Article ID 045501, 22 p. (2017). MSC: 76D05 76D03 PDF BibTeX XML Cite \textit{K. Ohkitani}, J. Phys. A, Math. Theor. 50, No. 4, Article ID 045501, 22 p. (2017; Zbl 1357.76015) Full Text: DOI OpenURL
Lichtenfelz, Leandro A. Nonuniqueness of solutions of the Navier-Stokes equations on Riemannian manifolds. (English) Zbl 1358.35095 Ann. Global Anal. Geom. 50, No. 3, 237-248 (2016). Reviewer: Gelu Paşa (Bucureşti) MSC: 35Q30 76D05 32Q05 PDF BibTeX XML Cite \textit{L. A. Lichtenfelz}, Ann. Global Anal. Geom. 50, No. 3, 237--248 (2016; Zbl 1358.35095) Full Text: DOI OpenURL
Ercan, Ali; Kavvas, M. Levent Self-similarity in incompressible Navier-Stokes equations. (English) Zbl 1374.76050 Chaos 25, No. 12, 123126, 5 p. (2015). MSC: 76D05 35Q86 PDF BibTeX XML Cite \textit{A. Ercan} and \textit{M. L. Kavvas}, Chaos 25, No. 12, 123126, 5 p. (2015; Zbl 1374.76050) Full Text: DOI OpenURL
Dascaliuc, Radu; Michalowski, Nicholas; Thomann, Enrique; Waymire, Edward C. Symmetry breaking and uniqueness for the incompressible Navier-Stokes equations. (English) Zbl 1374.76049 Chaos 25, No. 7, 075402, 16 p. (2015). MSC: 76D05 76D03 PDF BibTeX XML Cite \textit{R. Dascaliuc} et al., Chaos 25, No. 7, 075402, 16 p. (2015; Zbl 1374.76049) Full Text: DOI arXiv OpenURL
Chae, Dongho Remarks on the asymptotically discretely self-similar solutions of the Navier-Stokes and the Euler equations. (English) Zbl 1327.76022 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 125, 251-259 (2015). MSC: 76B03 35Q31 PDF BibTeX XML Cite \textit{D. Chae}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 125, 251--259 (2015; Zbl 1327.76022) Full Text: DOI arXiv OpenURL
Chae, Dongho Unique continuation type theorem for the self-similar Euler equations. (English) Zbl 1321.35145 Adv. Math. 283, 143-154 (2015). MSC: 35Q31 76B03 76W05 PDF BibTeX XML Cite \textit{D. Chae}, Adv. Math. 283, 143--154 (2015; Zbl 1321.35145) Full Text: DOI OpenURL
Chae, Dongho Euler’s equations and the maximum principle. (English) Zbl 1308.35185 Math. Ann. 361, No. 1-2, 51-66 (2015). MSC: 35Q31 76B03 76W05 35B50 35B45 PDF BibTeX XML Cite \textit{D. Chae}, Math. Ann. 361, No. 1--2, 51--66 (2015; Zbl 1308.35185) Full Text: DOI arXiv OpenURL
Song, Wenjing; Li, Hua; Yang, Ganshan; Yuan, George Xianzhi Nonhomogeneous boundary value problem for \((I, J)\) similar solutions of incompressible two-dimensional Euler equations. (English) Zbl 1335.35185 J. Inequal. Appl. 2014, Paper No. 277, 15 p. (2014). MSC: 35Q30 76D05 76D10 35B35 76D03 PDF BibTeX XML Cite \textit{W. Song} et al., J. Inequal. Appl. 2014, Paper No. 277, 15 p. (2014; Zbl 1335.35185) Full Text: DOI OpenURL
Benbernou, Samia; Ragusa, Maria Alessandra; Terbeche, Mekki Remarks on Leray’s self-similar solutions to the 3D magnetohydrodynamic equations. (English) Zbl 1317.35189 Math. Methods Appl. Sci. 37, No. 17, 2615-2618 (2014). MSC: 35Q35 35B65 76D05 76W05 35C06 PDF BibTeX XML Cite \textit{S. Benbernou} et al., Math. Methods Appl. Sci. 37, No. 17, 2615--2618 (2014; Zbl 1317.35189) Full Text: DOI OpenURL
Bradshaw, Zachary; Grujić, Zoran Blow-up scenarios for the 3D Navier-Stokes equations exhibiting sub-criticality with respect to the scaling of one-dimensional local sparseness. (English) Zbl 1293.35197 J. Math. Fluid Mech. 16, No. 2, 321-334 (2014). MSC: 35Q30 35B65 35B44 PDF BibTeX XML Cite \textit{Z. Bradshaw} and \textit{Z. Grujić}, J. Math. Fluid Mech. 16, No. 2, 321--334 (2014; Zbl 1293.35197) Full Text: DOI arXiv OpenURL
Tsai, Tai-Peng Forward discretely self-similar solutions of the Navier-Stokes equations. (English) Zbl 1293.35218 Commun. Math. Phys. 328, No. 1, 29-44 (2014). MSC: 35Q30 76D05 76D07 35B45 35C06 PDF BibTeX XML Cite \textit{T.-P. Tsai}, Commun. Math. Phys. 328, No. 1, 29--44 (2014; Zbl 1293.35218) Full Text: DOI arXiv OpenURL
Chae, Dongho Liouville-type theorems for the forced Euler equations and the Navier-Stokes equations. (English) Zbl 1285.35069 Commun. Math. Phys. 326, No. 1, 37-48 (2014). MSC: 35Q31 35Q30 76D05 35B53 PDF BibTeX XML Cite \textit{D. Chae}, Commun. Math. Phys. 326, No. 1, 37--48 (2014; Zbl 1285.35069) Full Text: DOI arXiv OpenURL
Campiti, Michele; Galdi, Giovanni P.; Hieber, Matthias Global existence of strong solutions for \(2\)-dimensional Navier-Stokes equations on exterior domains with growing data at infinity. (English) Zbl 1292.76028 Commun. Pure Appl. Anal. 13, No. 4, 1613-1627 (2014). MSC: 76D03 35Q30 35B30 PDF BibTeX XML Cite \textit{M. Campiti} et al., Commun. Pure Appl. Anal. 13, No. 4, 1613--1627 (2014; Zbl 1292.76028) Full Text: DOI OpenURL
Chae, Dongho; Shvydkoy, Roman On formation of a locally self-similar collapse in the incompressible Euler equations. (English) Zbl 1285.35070 Arch. Ration. Mech. Anal. 209, No. 3, 999-1017 (2013). Reviewer: Gheorghe Moroşanu (Budapest) MSC: 35Q31 35B44 PDF BibTeX XML Cite \textit{D. Chae} and \textit{R. Shvydkoy}, Arch. Ration. Mech. Anal. 209, No. 3, 999--1017 (2013; Zbl 1285.35070) Full Text: DOI arXiv OpenURL
Hsu, Pen-Yuan; Maekawa, Yasunori On nonexistence for stationary solutions to the Navier-Stokes equations with a linear strain. (English) Zbl 1409.76018 J. Math. Fluid Mech. 15, No. 2, 317-333 (2013). MSC: 76D03 35Q30 PDF BibTeX XML Cite \textit{P.-Y. Hsu} and \textit{Y. Maekawa}, J. Math. Fluid Mech. 15, No. 2, 317--333 (2013; Zbl 1409.76018) Full Text: DOI OpenURL
Galaktionov, V. A.; Maz’ya, V. Boundary characteristic point regularity for Navier-Stokes equations: blow-up scaling and petrovskii-type criterion (a formal approach). (English) Zbl 1248.35036 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75, No. 12, 4534-4559 (2012). Reviewer: Il’ya Sh. Mogilevskij (Tver’) MSC: 35B65 35Q30 PDF BibTeX XML Cite \textit{V. A. Galaktionov} and \textit{V. Maz'ya}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75, No. 12, 4534--4559 (2012; Zbl 1248.35036) Full Text: DOI arXiv OpenURL
Chae, Dongho On the self-similar solutions of the 3D Euler and the related equations. (English) Zbl 1219.35183 Commun. Math. Phys. 305, No. 2, 333-349 (2011). MSC: 35Q31 35Q30 76D05 35B44 35B40 PDF BibTeX XML Cite \textit{D. Chae}, Commun. Math. Phys. 305, No. 2, 333--349 (2011; Zbl 1219.35183) Full Text: DOI OpenURL
Kenig, Carlos E.; Koch, Gabriel S. An alternative approach to regularity for the Navier-Stokes equations in critical spaces. (English) Zbl 1220.35119 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 28, No. 2, 159-187 (2011). Reviewer: Keisuke Uchikoshi (Yokosuka) MSC: 35Q30 35B65 76D05 76D03 PDF BibTeX XML Cite \textit{C. E. Kenig} and \textit{G. S. Koch}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 28, No. 2, 159--187 (2011; Zbl 1220.35119) Full Text: DOI arXiv OpenURL
Maremonti, P. On the uniqueness of bounded very weak solutions to the Navier-Stokes Cauchy problem. (English) Zbl 1208.35105 Appl. Anal. 90, No. 1-2, 125-139 (2011). MSC: 35Q30 76D05 76D03 PDF BibTeX XML Cite \textit{P. Maremonti}, Appl. Anal. 90, No. 1--2, 125--139 (2011; Zbl 1208.35105) Full Text: DOI OpenURL
Chae, Dongho On the generalized self-similar singularities for the Euler and the Navier-Stokes equations. (English) Zbl 1189.35236 J. Funct. Anal. 258, No. 9, 2865-2883 (2010). MSC: 35Q31 35Q30 76D05 35B45 35B30 35B40 35B44 PDF BibTeX XML Cite \textit{D. Chae}, J. Funct. Anal. 258, No. 9, 2865--2883 (2010; Zbl 1189.35236) Full Text: DOI OpenURL
Kozono, Hideo; Sugiyama, Yoshie; Takada, Ryo Non-existence of finite-time self-similar solutions of the Keller-Segel system in the scaling invariant class. (English) Zbl 1188.35037 J. Math. Anal. Appl. 365, No. 1, 60-66 (2010). Reviewer: Philippe Laurençot (Toulouse) MSC: 35C06 35K45 92C17 35B44 35K58 PDF BibTeX XML Cite \textit{H. Kozono} et al., J. Math. Anal. Appl. 365, No. 1, 60--66 (2010; Zbl 1188.35037) Full Text: DOI OpenURL
Koch, Gabriel; Nadirashvili, Nikolai; Seregin, Gregory A.; Šverák, Vladimir Liouville theorems for the Navier-Stokes equations and applications. (English) Zbl 1208.35104 Acta Math. 203, No. 1, 83-105 (2009). Reviewer: Gelu Paşa (Bucureşti) MSC: 35Q30 35B53 76D05 PDF BibTeX XML Cite \textit{G. Koch} et al., Acta Math. 203, No. 1, 83--105 (2009; Zbl 1208.35104) Full Text: DOI arXiv OpenURL
Chen, Ping; Zhang, Ting Analytical solutions to the Navier-Stokes equations for non-Newtonian fluid. (English) Zbl 1212.35347 Appl. Math., Ser. B (Engl. Ed.) 24, No. 4, 483-489 (2009). MSC: 35Q30 PDF BibTeX XML Cite \textit{P. Chen} and \textit{T. Zhang}, Appl. Math., Ser. B (Engl. Ed.) 24, No. 4, 483--489 (2009; Zbl 1212.35347) Full Text: DOI OpenURL
Chae, Dongho Notes on the incompressible Euler and related equations on \(\mathbb R^N\). (English) Zbl 1189.35235 Chin. Ann. Math., Ser. B 30, No. 5, 513-526 (2009). MSC: 35Q31 35Q30 35B33 35B44 76D03 76N10 PDF BibTeX XML Cite \textit{D. Chae}, Chin. Ann. Math., Ser. B 30, No. 5, 513--526 (2009; Zbl 1189.35235) Full Text: DOI OpenURL
Li, Lu Isolated singularities of the 1D complex viscous Burgers equation. (English) Zbl 1180.35463 J. Dyn. Differ. Equations 21, No. 4, 623-630 (2009). MSC: 35Q53 35B44 35B65 PDF BibTeX XML Cite \textit{L. Li}, J. Dyn. Differ. Equations 21, No. 4, 623--630 (2009; Zbl 1180.35463) Full Text: DOI OpenURL
Chae, Dongho Nonexistence of self-similar singularities in the ideal magnetohydrodynamics. (English) Zbl 1252.76090 Arch. Ration. Mech. Anal. 194, No. 3, 1011-1027 (2009). MSC: 76W05 76M55 35Q35 35Q60 PDF BibTeX XML Cite \textit{D. Chae}, Arch. Ration. Mech. Anal. 194, No. 3, 1011--1027 (2009; Zbl 1252.76090) Full Text: DOI arXiv OpenURL
Chae, Dongho On the a priori estimates for the Euler, the Navier-Stokes and the quasi-geostrophic equations. (English) Zbl 1173.35094 Adv. Math. 221, No. 5, 1678-1702 (2009). Reviewer: Jürgen Socolowsky (Brandenburg an der Havel) MSC: 35Q30 76D05 35B45 86A05 PDF BibTeX XML Cite \textit{D. Chae}, Adv. Math. 221, No. 5, 1678--1702 (2009; Zbl 1173.35094) Full Text: DOI arXiv OpenURL
Seregin, G.; Šverák, V. On type I singularities of the local axi-symmetric solutions of the Navier-Stokes equations. (English) Zbl 1180.35002 Commun. Partial Differ. Equations 34, No. 2, 171-201 (2009). Reviewer: Oleg Dementiev (Chelyabinsk) MSC: 35-02 35Q30 76D05 76D03 PDF BibTeX XML Cite \textit{G. Seregin} and \textit{V. Šverák}, Commun. Partial Differ. Equations 34, No. 2, 171--201 (2009; Zbl 1180.35002) Full Text: DOI arXiv OpenURL
Galaktionov, V. A. On blow-up space jets for the Navier-Stokes equations in \(\mathbb R^{3}\) with convergence to Euler equations. (English) Zbl 1159.81322 J. Math. Phys. 49, No. 11, 113101, 28 p. (2008). MSC: 35Q30 35B44 76D05 PDF BibTeX XML Cite \textit{V. A. Galaktionov}, J. Math. Phys. 49, No. 11, 113101, 28 p. (2008; Zbl 1159.81322) Full Text: DOI OpenURL
Hou, Thomas Y.; Lei, Zhen; Li, Congming Global regularity of the 3D axi-symmetric Navier-Stokes equations with anisotropic data. (English) Zbl 1146.76010 Commun. Partial Differ. Equations 33, No. 9, 1622-1637 (2008). MSC: 76D03 76D05 35Q30 PDF BibTeX XML Cite \textit{T. Y. Hou} et al., Commun. Partial Differ. Equations 33, No. 9, 1622--1637 (2008; Zbl 1146.76010) Full Text: DOI arXiv OpenURL
Bae, Hyeong-Ohk; Jin, Bum Ja Regularity for the Navier-Stokes equations with slip boundary condition. (English) Zbl 1143.35079 Proc. Am. Math. Soc. 136, No. 7, 2439-2443 (2008). MSC: 35Q30 76D05 76D03 PDF BibTeX XML Cite \textit{H.-O. Bae} and \textit{B. J. Jin}, Proc. Am. Math. Soc. 136, No. 7, 2439--2443 (2008; Zbl 1143.35079) Full Text: DOI OpenURL
Chae, Dongho Nonexistence of self-similar singularities in the viscous magnetohydrodynamics with zero resistivity. (English) Zbl 1163.35030 J. Funct. Anal. 254, No. 2, 441-453 (2008). Reviewer: Jong Kyu Kim (Masan Kyungnam) MSC: 35Q35 PDF BibTeX XML Cite \textit{D. Chae}, J. Funct. Anal. 254, No. 2, 441--453 (2008; Zbl 1163.35030) Full Text: DOI arXiv OpenURL
Miao, Changxing; Yuan, Baoquan Weak Morrey spaces and strong solutions to the Navier-Stokes equations. (English) Zbl 1149.35071 Sci. China, Ser. A 50, No. 10, 1401-1417 (2007). Reviewer: Il’ya Sh. Mogilevskij (Tver’) MSC: 35Q30 76D05 46E35 PDF BibTeX XML Cite \textit{C. Miao} and \textit{B. Yuan}, Sci. China, Ser. A 50, No. 10, 1401--1417 (2007; Zbl 1149.35071) Full Text: DOI OpenURL
Chae, Dongho Nonexistence of asymptotically self-similar singularities in the Euler and the Navier-Stokes equations. (English) Zbl 1147.35068 Math. Ann. 338, No. 2, 435-449 (2007). Reviewer: Thomas Hagen (Memphis) MSC: 35Q30 35Q35 35B60 76D05 76D03 PDF BibTeX XML Cite \textit{D. Chae}, Math. Ann. 338, No. 2, 435--449 (2007; Zbl 1147.35068) Full Text: DOI arXiv OpenURL
Chae, Dongho Nonexistence of self-similar singularities for the 3D incompressible Euler equations. (English) Zbl 1157.35079 Commun. Math. Phys. 273, No. 1, 203-215 (2007). Reviewer: Il’ya Sh. Mogilevskij (Tver’) MSC: 35Q05 76B03 35B40 35Q30 PDF BibTeX XML Cite \textit{D. Chae}, Commun. Math. Phys. 273, No. 1, 203--215 (2007; Zbl 1157.35079) Full Text: DOI arXiv OpenURL
Dindoŝ, Martin; Mitrea, Marius The stationary Navier-Stokes system in nonsmooth manifolds: the Poisson problem in Lipschitz and \(C^{1}\) domains. (English) Zbl 1059.76014 Arch. Ration. Mech. Anal. 174, No. 1, 1-47 (2004). MSC: 76D03 35Q30 PDF BibTeX XML Cite \textit{M. Dindoŝ} and \textit{M. Mitrea}, Arch. Ration. Mech. Anal. 174, No. 1, 1--47 (2004; Zbl 1059.76014) Full Text: DOI OpenURL
Plecháč, Petr; Šverák, Vladimír On self-similar singular solutions of the complex Ginzburg-Landau equation. (English) Zbl 1032.35162 Commun. Pure Appl. Math. 54, No. 10, 1215-1242 (2001). MSC: 35Q55 35A20 37K40 PDF BibTeX XML Cite \textit{P. Plecháč} and \textit{V. Šverák}, Commun. Pure Appl. Math. 54, No. 10, 1215--1242 (2001; Zbl 1032.35162) Full Text: DOI arXiv OpenURL
Ishikawa, Masayoshi; Matsui, Shin’ya Existence of a forward self-similar stagnation flow of the Navier-Stokes equations. (English) Zbl 1306.76015 Japan J. Ind. Appl. Math. 17, No. 1, 19-25 (2000). MSC: 76D05 76D03 35Q30 PDF BibTeX XML Cite \textit{M. Ishikawa} and \textit{S. Matsui}, Japan J. Ind. Appl. Math. 17, No. 1, 19--25 (2000; Zbl 1306.76015) Full Text: DOI OpenURL
Šverák, Vladimír; Tsai, Tai-Peng On the spatial decay of 3-D steady-state Navier-Stokes flows. (English) Zbl 0971.35059 Commun. Partial Differ. Equations 25, No. 11-12, 2107-2117 (2000). Reviewer: Oleg Titow (Berlin) MSC: 35Q30 76D03 76D05 PDF BibTeX XML Cite \textit{V. Šverák} and \textit{T.-P. Tsai}, Commun. Partial Differ. Equations 25, No. 11--12, 2107--2117 (2000; Zbl 0971.35059) Full Text: DOI OpenURL