Wang, Ran; Zhang, Huai; Kang, Tong A formulation for a nonlinear axisymmetric magneto-heat coupling problem with an unknown nonlocal boundary condition. (English) Zbl 07804042 Comput. Methods Appl. Math. 24, No. 1, 239-264 (2024). MSC: 35Q60 35Q79 78A30 80A19 35A01 35A02 35B07 35D30 35A15 65M60 65M20 65N30 65M12 PDFBibTeX XMLCite \textit{R. Wang} et al., Comput. Methods Appl. Math. 24, No. 1, 239--264 (2024; Zbl 07804042) Full Text: DOI
Guo, Zhengguang; Chen, Fangru Regularity via one vorticity component for the 3D axisymmetric MHD equations. (English) Zbl 1527.35282 Math. Nachr. 296, No. 2, 675-688 (2023). MSC: 35Q35 76D05 76W05 76D17 35B65 35B07 35D30 42B25 PDFBibTeX XMLCite \textit{Z. Guo} and \textit{F. Chen}, Math. Nachr. 296, No. 2, 675--688 (2023; Zbl 1527.35282) Full Text: DOI
Chen, Hui; Tsai, Tai-Peng; Zhang, Ting Remarks on local regularity of axisymmetric solutions to the 3D Navier-Stokes equations. (English) Zbl 1492.35219 Commun. Partial Differ. Equations 47, No. 8, 1680-1699 (2022); correction ibid. 48, No. 6, 987-988 (2023). MSC: 35Q35 35Q30 76D03 PDFBibTeX XMLCite \textit{H. Chen} et al., Commun. Partial Differ. Equations 47, No. 8, 1680--1699 (2022; Zbl 1492.35219) Full Text: DOI arXiv
Liu, Shuzhi; Zhang, Qinglong Axisymmetric solutions of the shallow water equations with bottom topography. (English) Zbl 1507.35191 Res. Math. Sci. 9, No. 1, Paper No. 17, 17 p. (2022). MSC: 35Q35 76B15 76B03 35A24 35B07 35C06 35D30 35A01 PDFBibTeX XMLCite \textit{S. Liu} and \textit{Q. Zhang}, Res. Math. Sci. 9, No. 1, Paper No. 17, 17 p. (2022; Zbl 1507.35191) Full Text: DOI
Fernández-Dalgo, Pedro Gabriel; Lemarié-Rieusset, Pierre Gilles Weighted energy estimates for the incompressible Navier-Stokes equations and applications to axisymmetric solutions without swirl. (English) Zbl 1479.35610 J. Math. Fluid Mech. 23, No. 3, Paper No. 76, 20 p. (2021). MSC: 35Q30 76D05 76D17 35B07 35D30 35A01 PDFBibTeX XMLCite \textit{P. G. Fernández-Dalgo} and \textit{P. G. Lemarié-Rieusset}, J. Math. Fluid Mech. 23, No. 3, Paper No. 76, 20 p. (2021; Zbl 1479.35610) Full Text: DOI arXiv
Jiu, Quansen; Liu, Jitao; Niu, Dongjuan Global existence of weak solutions to the incompressible axisymmetric Euler equations without swirl. (English) Zbl 1462.35271 J. Nonlinear Sci. 31, No. 2, Paper No. 36, 24 p. (2021). MSC: 35Q31 76B03 76B47 35D30 35B07 35B65 PDFBibTeX XMLCite \textit{Q. Jiu} et al., J. Nonlinear Sci. 31, No. 2, Paper No. 36, 24 p. (2021; Zbl 1462.35271) Full Text: DOI arXiv
Wang, Shu; Wang, Yongxin; Liu, Jitao Regularity criteria to the incompressible axisymmetric Boussinesq equations. (English) Zbl 1454.35304 Appl. Math. Lett. 112, Article ID 106800, 7 p. (2021). MSC: 35Q35 76D05 35B65 35B45 35B07 35D30 PDFBibTeX XMLCite \textit{S. Wang} et al., Appl. Math. Lett. 112, Article ID 106800, 7 p. (2021; Zbl 1454.35304) Full Text: DOI
Seregin, G. Local regularity of axisymmetric solutions to the Navier-Stokes equations. (English) Zbl 1450.35097 Anal. Math. Phys. 10, No. 4, Paper No. 46, 19 p. (2020). MSC: 35B65 35Q30 35D30 76D03 PDFBibTeX XMLCite \textit{G. Seregin}, Anal. Math. Phys. 10, No. 4, Paper No. 46, 19 p. (2020; Zbl 1450.35097) Full Text: DOI arXiv
Abe, Ken Vanishing viscosity limits for axisymmetric flows with boundary. (English. French summary) Zbl 1437.35562 J. Math. Pures Appl. (9) 137, 1-32 (2020). MSC: 35Q35 35K90 76B03 76D05 35D30 35B07 35A01 35A02 35Q31 PDFBibTeX XMLCite \textit{K. Abe}, J. Math. Pures Appl. (9) 137, 1--32 (2020; Zbl 1437.35562) Full Text: DOI arXiv
Makino, Tetu On slowly rotating axisymmetric solutions of the Einstein-Euler equations. (English) Zbl 1402.83029 J. Math. Phys. 59, No. 10, 102502, 33 p. (2018). MSC: 83C15 83C05 83C55 76Y05 76U05 85A25 85A15 83C25 PDFBibTeX XMLCite \textit{T. Makino}, J. Math. Phys. 59, No. 10, 102502, 33 p. (2018; Zbl 1402.83029) Full Text: DOI arXiv
Deng, Xuemei; Wang, Tian-Yi; Xiang, Wei Three-dimensional full Euler flows with nontrivial swirl in axisymmetric nozzles. (English) Zbl 1393.35153 SIAM J. Math. Anal. 50, No. 3, 2740-2772 (2018). Reviewer: Gelu Paşa (Bucureşti) MSC: 35Q31 35M30 35L65 76N10 76G25 35B40 35D30 35B07 PDFBibTeX XMLCite \textit{X. Deng} et al., SIAM J. Math. Anal. 50, No. 3, 2740--2772 (2018; Zbl 1393.35153) Full Text: DOI
Molina, Alfred; Ruiz, E. An approximate global solution of Einstein’s equations for a differentially rotating compact body. (English) Zbl 1380.83056 Gen. Relativ. Gravitation 49, No. 10, Paper No. 135, 13 p. (2017). MSC: 83C15 53Z05 83C25 85A15 PDFBibTeX XMLCite \textit{A. Molina} and \textit{E. Ruiz}, Gen. Relativ. Gravitation 49, No. 10, Paper No. 135, 13 p. (2017; Zbl 1380.83056) Full Text: DOI arXiv
Martín, Jesús; Molina, Alfred; Ruiz, Eduardo Perturbation theory and harmonic gauge propagation in general relativity, a particular example. (English) Zbl 1327.83070 Gen. Relativ. Gravitation 47, No. 10, Paper No. 112, 21 p. (2015). MSC: 83C15 83C05 53Z05 83C25 83C55 PDFBibTeX XMLCite \textit{J. Martín} et al., Gen. Relativ. Gravitation 47, No. 10, Paper No. 112, 21 p. (2015; Zbl 1327.83070) Full Text: DOI arXiv Link
Prabhu, Kartik; Wald, Robert M. Black hole instabilities and exponential growth. (English) Zbl 1326.83053 Commun. Math. Phys. 340, No. 1, 253-290 (2015). MSC: 83C57 83C75 83C05 83C25 83C15 81T30 47B25 83E15 83C40 PDFBibTeX XMLCite \textit{K. Prabhu} and \textit{R. M. Wald}, Commun. Math. Phys. 340, No. 1, 253--290 (2015; Zbl 1326.83053) Full Text: DOI arXiv
Jiu, Quansen; Wu, Jiahong; Yang, Wanrong Viscous approximation and weak solutions of the 3D axisymmetric Euler equations. (English) Zbl 1307.35226 Math. Methods Appl. Sci. 38, No. 3, 548-558 (2015). MSC: 35Q35 76D03 PDFBibTeX XMLCite \textit{Q. Jiu} et al., Math. Methods Appl. Sci. 38, No. 3, 548--558 (2015; Zbl 1307.35226) Full Text: DOI
Bermúdez, A.; Gómez, D.; Rodríguez, R.; Venegas, P. Mathematical analysis and numerical solution of axisymmetric eddy-current problems with Preisach hysteresis model. (English) Zbl 1366.78004 Rend. Semin. Mat., Univ. Politec. Torino 72, No. 1-2, 73-117 (2014). Reviewer: Teodora-Liliana Rădulescu (Craiova) MSC: 78A25 65N30 78A55 78M10 78M20 65N15 35D30 47J40 PDFBibTeX XMLCite \textit{A. Bermúdez} et al., Rend. Semin. Mat., Univ. Politec. Torino 72, No. 1--2, 73--117 (2014; Zbl 1366.78004)
Mars, Marc; Mena, Filipe C.; Vera, Raül Review on exact and perturbative deformations of the Einstein-Straus model: uniqueness and rigidity results. (English) Zbl 1274.83167 Gen. Relativ. Gravitation 45, No. 11, 2143-2173 (2013). MSC: 83F05 83C15 83C25 83-02 PDFBibTeX XMLCite \textit{M. Mars} et al., Gen. Relativ. Gravitation 45, No. 11, 2143--2173 (2013; Zbl 1274.83167) Full Text: DOI arXiv
Bardos, C.; Lopes Filho, M. C.; Niu, Dongjuan; Nussenzveig Lopes, H. J.; Titi, E. S. Stability of two-dimensional viscous incompressible flows under three-dimensional perturbations and inviscid symmetry breaking. (English) Zbl 1291.35207 SIAM J. Math. Anal. 45, No. 3, 1871-1885 (2013). MSC: 35Q35 65M70 PDFBibTeX XMLCite \textit{C. Bardos} et al., SIAM J. Math. Anal. 45, No. 3, 1871--1885 (2013; Zbl 1291.35207) Full Text: DOI arXiv
Yuan, Bao-Quan; Li, Feng-Ping Regularity criteria of axisymmetric weak solutions to the 3D magnetohydrodynamic equations. (English) Zbl 1329.35256 Acta Math. Appl. Sin., Engl. Ser. 29, No. 2, 289-302 (2013). MSC: 35Q35 35B65 35D30 76W05 PDFBibTeX XMLCite \textit{B.-Q. Yuan} and \textit{F.-P. Li}, Acta Math. Appl. Sin., Engl. Ser. 29, No. 2, 289--302 (2013; Zbl 1329.35256) Full Text: DOI
Li, Fengping A regularity criterion to the weak solutions of the generalized magnetohydrodynamic equations. (Chinese. English summary) Zbl 1289.35041 Pure Appl. Math. 28, No. 6, 735-743 (2012). MSC: 35B65 35D30 76W05 PDFBibTeX XMLCite \textit{F. Li}, Pure Appl. Math. 28, No. 6, 735--743 (2012; Zbl 1289.35041)
Li, Fengping; Yuan, Baoquan Regularity criteria to the axisymmetric solutions of generalized magneto-hydrodynamic equations. (Chinese. English summary) Zbl 1228.76192 Appl. Math., Ser. A (Chin. Ed.) 25, No. 3, 319-325 (2010). MSC: 76W05 35B65 PDFBibTeX XMLCite \textit{F. Li} and \textit{B. Yuan}, Appl. Math., Ser. A (Chin. Ed.) 25, No. 3, 319--325 (2010; Zbl 1228.76192)
Chen, Chiun-Chuan; Strain, Robert M.; Yau, Horng-Tzer; Tsai, Tai-Peng Lower bound on the blow-up rate of the axisymmetric Navier-Stokes equations. (English) Zbl 1154.35068 Int. Math. Res. Not. 2008, Article ID rnn016, 31 p. (2008). Reviewer: Pavel Burda (Praha) MSC: 35Q30 35B05 76D05 76D03 35B65 35D10 PDFBibTeX XMLCite \textit{C.-C. Chen} et al., Int. Math. Res. Not. 2008, Article ID rnn016, 31 p. (2008; Zbl 1154.35068) Full Text: DOI arXiv
Jiang, Song; Zhang, Ping Axisymmetric solutions of the 3D Navier-Stokes equations for compressible isentropic fluids. (English) Zbl 1109.35088 J. Math. Pures Appl. (9) 82, No. 8, 949-973 (2003). MSC: 35Q30 35D05 76N10 PDFBibTeX XMLCite \textit{S. Jiang} and \textit{P. Zhang}, J. Math. Pures Appl. (9) 82, No. 8, 949--973 (2003; Zbl 1109.35088) Full Text: DOI
Pokorný, Milan A regularity criterion for the angular velocity component in the case of axisymmetric Navier-Stokes equations. (English) Zbl 1033.35085 Bemelmans, Josef (ed.) et al., Elliptic and parabolic problems. Proceedings of the 4th European conference, Rolduc, Netherlands, June 18–22, 2001 and Gaeta, Italy, September 24–28, 2001. Singapore: World Scientific (ISBN 981-238-045-0/hbk). 233-242 (2002). MSC: 35Q30 76D03 35D10 PDFBibTeX XMLCite \textit{M. Pokorný}, in: Elliptic and parabolic problems. Proceedings of the 4th European conference, Rolduc, Netherlands, June 18--22, 2001 and Gaeta, Italy, September 24--28, 2001. Singapore: World Scientific. 233--242 (2002; Zbl 1033.35085)
Chae, Dongho; Lee, Jihoon On the regularity of the axisymmetric solutions of the Navier-Stokes equations. (English) Zbl 0992.35068 Math. Z. 239, No. 4, 645-671 (2002). MSC: 35Q30 76D03 76D05 PDFBibTeX XMLCite \textit{D. Chae} and \textit{J. Lee}, Math. Z. 239, No. 4, 645--671 (2002; Zbl 0992.35068) Full Text: DOI
Chae, Dongho; Lee, Jihoon Regularity criteria of the axisymmetric Navier-Stokes equations. (English) Zbl 0991.35063 Salvi, Rodolfo (ed.), The Navier-Stokes equations: theory and numerical methods. Proceedings of the international conference, Varenna, Lecco, Italy, 2000. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 223, 159-165 (2002). MSC: 35Q30 35B65 35B45 PDFBibTeX XMLCite \textit{D. Chae} and \textit{J. Lee}, Lect. Notes Pure Appl. Math. 223, 159--165 (2002; Zbl 0991.35063)
Hoenselaers, C. Factor structure of the Tomimatsu-Sato solutions and their recurrence relations. (English) Zbl 0965.83011 Ann. Phys. (8) 9, No. 6, 453-460 (2000). MSC: 83C15 83C80 83C25 PDFBibTeX XMLCite \textit{C. Hoenselaers}, Ann. Phys. (8) 9, No. 6, 453--460 (2000; Zbl 0965.83011) Full Text: DOI
Klein, C.; Richter, O. Stationary axisymmetric dust disks and hyperelliptic Riemann surfaces. (English) Zbl 0963.83019 Piran, Tsvi (ed.), The 8th Marcel Grossmann meeting on recent developments in theoretical and experimental general relativity, gravitation and relativistic field theories. Proceedings of the meeting held in Jerusalem, Israel, June 22-27, 1997. In 2 vols. Singapore: World Scientific. 336-338 (1999). MSC: 83C55 83C25 83C20 PDFBibTeX XMLCite \textit{C. Klein} and \textit{O. Richter}, in: The 8th Marcel Grossmann meeting on recent developments in theoretical and experimental general relativity, gravitation and relativistic field theories. Proceedings of the meeting held in Jerusalem, Israel, June 22--27, 1997. In 2 vols. Singapore: World Scientific. 336--338 (1999; Zbl 0963.83019)
Kuang, Weijia; Bloxham, Jeremy Numerical modeling of magnetohydrodynamic convection in a rapidly rotating spherical shell: Weak and strong field dynamo action. (English) Zbl 0957.76096 J. Comput. Phys. 153, No. 1, 51-81 (1999). MSC: 76W05 76U05 76M22 76M20 86A25 65Y05 PDFBibTeX XMLCite \textit{W. Kuang} and \textit{J. Bloxham}, J. Comput. Phys. 153, No. 1, 51--81 (1999; Zbl 0957.76096) Full Text: DOI
Erlebacher, G.; Hussaini, M. Y.; Shu, C.-W. Interaction of a shock with a longitudinal vortex. (English) Zbl 0889.76033 J. Fluid Mech. 337, 129-153 (1997). MSC: 76L05 76N10 76M20 PDFBibTeX XMLCite \textit{G. Erlebacher} et al., J. Fluid Mech. 337, 129--153 (1997; Zbl 0889.76033) Full Text: DOI
Berger, Melvyn S. Sobolev space methods for three dimensional solitons of the Euler equations. (English. Abridged French version) Zbl 0782.35057 C. R. Acad. Sci., Paris, Sér. I 317, No. 8, 755-760 (1993). MSC: 35Q35 76B47 35D05 PDFBibTeX XMLCite \textit{M. S. Berger}, C. R. Acad. Sci., Paris, Sér. I 317, No. 8, 755--760 (1993; Zbl 0782.35057)