Deng, Dingqun; Duan, Renjun Low regularity solutions for the Vlasov-Poisson-Landau/Boltzmann system. (English) Zbl 1511.35252 Nonlinearity 36, No. 5, 2193-2248 (2023). MSC: 35Q20 35Q83 35J05 76X05 82C22 82C40 35B65 35A01 PDFBibTeX XMLCite \textit{D. Deng} and \textit{R. Duan}, Nonlinearity 36, No. 5, 2193--2248 (2023; Zbl 1511.35252) Full Text: DOI arXiv
Deng, Dingqun; Duan, Renjun Spectral gap formation to kinetic equations with soft potentials in bounded domain. (English) Zbl 1508.35032 Commun. Math. Phys. 397, No. 3, 1441-1489 (2023). MSC: 35Q20 82C40 35P15 76P05 PDFBibTeX XMLCite \textit{D. Deng} and \textit{R. Duan}, Commun. Math. Phys. 397, No. 3, 1441--1489 (2023; Zbl 1508.35032) Full Text: DOI arXiv
Duan, Renjun; Li, Wei-Xi; Liu, Lvqiao Gevrey regularity of mild solutions to the non-cutoff Boltzmann equation. (English) Zbl 1481.35303 Adv. Math. 395, Article ID 108159, 75 p. (2022). MSC: 35Q20 35B65 35B20 35H10 35A01 35A02 82C40 PDFBibTeX XMLCite \textit{R. Duan} et al., Adv. Math. 395, Article ID 108159, 75 p. (2022; Zbl 1481.35303) Full Text: DOI arXiv
Duan, Renjun; Liu, Shuangqian The Boltzmann equation for uniform shear flow. (English) Zbl 1477.76075 Arch. Ration. Mech. Anal. 242, No. 3, 1947-2002 (2021). MSC: 76P05 35Q20 35Q35 82C40 PDFBibTeX XMLCite \textit{R. Duan} and \textit{S. Liu}, Arch. Ration. Mech. Anal. 242, No. 3, 1947--2002 (2021; Zbl 1477.76075) Full Text: DOI arXiv
Duan, Renjun; Liu, Shuangqian Compressible Navier-Stokes approximation for the Boltzmann equation in bounded domains. (English) Zbl 1479.35661 Trans. Am. Math. Soc. 374, No. 11, 7867-7924 (2021). MSC: 35Q35 35Q31 35Q20 76P05 76N06 82C40 35B65 35A01 PDFBibTeX XMLCite \textit{R. Duan} and \textit{S. Liu}, Trans. Am. Math. Soc. 374, No. 11, 7867--7924 (2021; Zbl 1479.35661) Full Text: DOI arXiv
Duan, Renjun; Liu, Shuangqian; Sakamoto, Shota; Strain, Robert M. Global mild solutions of the Landau and non-cutoff Boltzmann equations. (English) Zbl 1476.35161 Commun. Pure Appl. Math. 74, No. 5, 932-1020 (2021). Reviewer: Eugene Postnikov (Kursk) MSC: 35Q20 35Q82 35B65 35A01 35A02 82C22 82C40 PDFBibTeX XMLCite \textit{R. Duan} et al., Commun. Pure Appl. Math. 74, No. 5, 932--1020 (2021; Zbl 1476.35161) Full Text: DOI arXiv
Duan, Renjun; Yang, Dongcheng; Yu, Hongjun Small Knudsen rate of convergence to rarefaction wave for the Landau equation. (English) Zbl 1467.82074 Arch. Ration. Mech. Anal. 240, No. 3, 1535-1592 (2021). MSC: 82C40 35Q20 76P05 35Q31 PDFBibTeX XMLCite \textit{R. Duan} et al., Arch. Ration. Mech. Anal. 240, No. 3, 1535--1592 (2021; Zbl 1467.82074) Full Text: DOI arXiv
Duan, Renjun; Liu, Shuangqian; Sakamoto, Shota; Strain, Robert M. Global solutions to the Boltzmann equation without angular cutoff and the Landau equation with Coulomb potential. (English) Zbl 1455.35166 RIMS Kôkyûroku Bessatsu B82, 29-46 (2020). MSC: 35Q20 82D10 82C40 35A01 PDFBibTeX XMLCite \textit{R. Duan} et al., RIMS Kôkyûroku Bessatsu B82, 29--46 (2020; Zbl 1455.35166) Full Text: Link
Duan, Renjun; Huang, Feimin; Wang, Yong; Zhang, Zhu Effects of soft interaction and non-isothermal boundary upon long-time dynamics of rarefied gas. (English) Zbl 1428.35265 Arch. Ration. Mech. Anal. 234, No. 2, 925-1006 (2019). MSC: 35Q20 82C40 76N15 76P05 35B40 35B35 35A01 PDFBibTeX XMLCite \textit{R. Duan} et al., Arch. Ration. Mech. Anal. 234, No. 2, 925--1006 (2019; Zbl 1428.35265) Full Text: DOI arXiv
Duan, Renjun; Sakamoto, Shota Solution to the Boltzmann equation in velocity-weighted Chemin-Lerner type spaces. (English) Zbl 1405.35127 Kinet. Relat. Models 11, No. 6, 1301-1331 (2018). MSC: 35Q20 76P05 82B40 PDFBibTeX XMLCite \textit{R. Duan} and \textit{S. Sakamoto}, Kinet. Relat. Models 11, No. 6, 1301--1331 (2018; Zbl 1405.35127) Full Text: DOI arXiv
Duan, Renjun; Wang, Yong; Yang, Tong Global existence for the ellipsoidal BGK model with initial large oscillations. (Chinese. English summary) Zbl 1499.35465 Sci. Sin., Math. 47, No. 10, 1143-1154 (2017). MSC: 35Q20 35Q82 82C40 PDFBibTeX XMLCite \textit{R. Duan} et al., Sci. Sin., Math. 47, No. 10, 1143--1154 (2017; Zbl 1499.35465) Full Text: DOI arXiv
Duan, Renjun; Liu, Shuangqian The Vlasov-Poisson-Boltzmann system for a disparate mass binary mixture. (English) Zbl 1393.35245 J. Stat. Phys. 169, No. 3, 614-684 (2017). Reviewer: Dmitry Pelinovsky (Hamilton) MSC: 35Q83 35Q20 76P05 35B35 35B40 82D10 PDFBibTeX XMLCite \textit{R. Duan} and \textit{S. Liu}, J. Stat. Phys. 169, No. 3, 614--684 (2017; Zbl 1393.35245) Full Text: DOI arXiv
Duan, Renjun; Yu, Hongjun The relativistic Boltzmann equation for soft potentials. (English) Zbl 1367.35098 Adv. Math. 312, 315-373 (2017). MSC: 35Q20 35Q75 35B40 35B65 82C40 PDFBibTeX XMLCite \textit{R. Duan} and \textit{H. Yu}, Adv. Math. 312, 315--373 (2017; Zbl 1367.35098) Full Text: DOI
Duan, Renjun; Lei, Yuanjie; Yang, Tong; Zhao, Huijiang The Vlasov-Maxwell-Boltzmann system near Maxwellians in the whole space with very soft potentials. (English) Zbl 1414.82027 Commun. Math. Phys. 351, No. 1, 95-153 (2017). Reviewer: Dominik Strzałka (Rzeszów) MSC: 82C40 35Q83 35Q61 35Q20 35L60 35A01 PDFBibTeX XMLCite \textit{R. Duan} et al., Commun. Math. Phys. 351, No. 1, 95--153 (2017; Zbl 1414.82027) Full Text: DOI arXiv
Duan, RenJun; Liu, ShuangQian; Yin, HaiYan; Zhu, ChangJiang Stability of the rarefaction wave for a two-fluid plasma model with diffusion. (English) Zbl 1362.35038 Sci. China, Math. 59, No. 1, 67-84 (2016). Reviewer: Simonetta Abenda (Bologna) MSC: 35B35 35B40 35Q35 82D10 76X05 35Q31 PDFBibTeX XMLCite \textit{R. Duan} et al., Sci. China, Math. 59, No. 1, 67--84 (2016; Zbl 1362.35038) Full Text: DOI
Duan, Renjun; Liu, Shuangqian Time-periodic solutions of the Vlasov-Poisson-Fokker-Planck system. (English) Zbl 1340.35348 Acta Math. Sci., Ser. B, Engl. Ed. 35, No. 4, 876-886 (2015). MSC: 35Q84 82D10 PDFBibTeX XMLCite \textit{R. Duan} and \textit{S. Liu}, Acta Math. Sci., Ser. B, Engl. Ed. 35, No. 4, 876--886 (2015; Zbl 1340.35348) Full Text: DOI
Duan, Renjun; Liu, Shuangqian Stability of the rarefaction wave of the Vlasov-Poisson-Boltzmann system. (English) Zbl 1326.35221 SIAM J. Math. Anal. 47, No. 5, 3585-3647 (2015). Reviewer: Thomas Ernst (Uppsala) MSC: 35Q20 35Q83 35B35 35B40 82D10 PDFBibTeX XMLCite \textit{R. Duan} and \textit{S. Liu}, SIAM J. Math. Anal. 47, No. 5, 3585--3647 (2015; Zbl 1326.35221) Full Text: DOI arXiv
Duan, Renjun Global smooth dynamics of a fully ionized plasma with long-range collisions. (English) Zbl 1305.82057 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 31, No. 4, 751-778 (2014). Reviewer: Claudia-Veronika Meister (Darmstadt) MSC: 82D10 35Q84 35Q83 PDFBibTeX XMLCite \textit{R. Duan}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 31, No. 4, 751--778 (2014; Zbl 1305.82057) Full Text: DOI arXiv
Duan, Renjun; Liu, Shuangqian The Vlasov-Poisson-Boltzmann system without angular cutoff. (English) Zbl 1285.35115 Commun. Math. Phys. 324, No. 1, 1-45 (2013). Reviewer: Oleg A. Sinkevich (Moskva) MSC: 35Q60 35Q83 35Q20 82D10 PDFBibTeX XMLCite \textit{R. Duan} and \textit{S. Liu}, Commun. Math. Phys. 324, No. 1, 1--45 (2013; Zbl 1285.35115) Full Text: DOI arXiv
Duan, Renjun; Liu, Shuangqian; Yang, Tong; Zhao, Huijiang Stability of the nonrelativistic Vlasov-Maxwell-Boltzmann system for angular non-cutoff potentials. (English) Zbl 1288.35476 Kinet. Relat. Models 6, No. 1, 159-204 (2013). Reviewer: Vladimir Čadež (Beograd) MSC: 35Q83 35Q61 35Q20 35B35 82D10 76P05 PDFBibTeX XMLCite \textit{R. Duan} et al., Kinet. Relat. Models 6, No. 1, 159--204 (2013; Zbl 1288.35476) Full Text: DOI
Duan, Renjun; Yang, Tong; Zhao, Huijiang The Vlasov-Poisson-Boltzmann system in the whole space: The hard potential case. (English) Zbl 1247.35174 J. Differ. Equations 252, No. 12, 6356-6386 (2012). Reviewer: Stephen Wollman (New York) MSC: 35Q83 35Q20 82C40 82D10 PDFBibTeX XMLCite \textit{R. Duan} et al., J. Differ. Equations 252, No. 12, 6356--6386 (2012; Zbl 1247.35174) Full Text: DOI
Duan, Renjun; Yang, Tong Stability of the one-species Vlasov-Poisson-Boltzmann system. (English) Zbl 1323.82036 SIAM J. Math. Anal. 41, No. 6, 2353-2387 (2010). MSC: 82C40 35Q83 76P05 82D05 PDFBibTeX XMLCite \textit{R. Duan} and \textit{T. Yang}, SIAM J. Math. Anal. 41, No. 6, 2353--2387 (2010; Zbl 1323.82036) Full Text: DOI
Duan, Renjun; Fornasier, Massimo; Toscani, Giuseppe A kinetic flocking model with diffusion. (English) Zbl 1213.35395 Commun. Math. Phys. 300, No. 1, 95-145 (2010). Reviewer: Giovanni Mascali (Arcavacata di Rende) MSC: 35Q84 82B05 35Q82 35A01 35B35 35B40 PDFBibTeX XMLCite \textit{R. Duan} et al., Commun. Math. Phys. 300, No. 1, 95--145 (2010; Zbl 1213.35395) Full Text: DOI
Duan, Renjun Stability of the Boltzmann equation with potential forces on torus. (English) Zbl 1173.35638 Physica D 238, No. 17, 1808-1820 (2009). MSC: 35Q35 76P05 82B40 35B35 PDFBibTeX XMLCite \textit{R. Duan}, Physica D 238, No. 17, 1808--1820 (2009; Zbl 1173.35638) Full Text: DOI
Duan, Renjun On the Cauchy problem for the Boltzmann equation in the whole space: Global existence and uniform stability in \(L_{\xi}^{2}(H_{x}^{N})\). (English) Zbl 1150.82019 J. Differ. Equations 244, No. 12, 3204-3234 (2008). Reviewer: Oleg A. Sinkevich (Moskva) MSC: 82C40 82D05 76P05 PDFBibTeX XMLCite \textit{R. Duan}, J. Differ. Equations 244, No. 12, 3204--3234 (2008; Zbl 1150.82019) Full Text: DOI
Duan, Renjun; Ukai, Seiji; Yang, Tong; Zhao, Huijiang Optimal decay estimates on the linearized Boltzmann equation with time dependent force and their applications. (English) Zbl 1175.82047 Commun. Math. Phys. 277, No. 1, 189-236 (2008). Reviewer: Bernard Ducomet (Bruyères le Châtel) MSC: 82C40 35Q35 35B30 76D03 76D05 PDFBibTeX XMLCite \textit{R. Duan} et al., Commun. Math. Phys. 277, No. 1, 189--236 (2008; Zbl 1175.82047) Full Text: DOI
Duan, Renjun; Yang, Tong; Zhu, Changjiang Existence of stationary solutions to the Vlasov-Poisson-Boltzmann system. (English) Zbl 1253.82079 J. Math. Anal. Appl. 327, No. 1, 425-434 (2007). MSC: 82D10 35Q83 35J60 76P05 76X05 82C40 PDFBibTeX XMLCite \textit{R. Duan} et al., J. Math. Anal. Appl. 327, No. 1, 425--434 (2007; Zbl 1253.82079) Full Text: DOI
Duan, Renjun; Yang, Tong; Zhu, Changjiang Boltzmann equation with external force and Vlasov-Poisson-Boltzmann system in infinite vacuum. (English) Zbl 1185.35035 Discrete Contin. Dyn. Syst. 16, No. 1, 253-277 (2006). MSC: 35F25 35Q20 76P05 82C40 PDFBibTeX XMLCite \textit{R. Duan} et al., Discrete Contin. Dyn. Syst. 16, No. 1, 253--277 (2006; Zbl 1185.35035) Full Text: DOI
Duan, Renjun; Yang, Tong; Zhu, Changjiang Global existence to Boltzmann equation with external force in infinite vacuum. (English) Zbl 1110.82034 J. Math. Phys. 46, No. 5, 053307, 13 p. (2005). MSC: 82C40 82B40 PDFBibTeX XMLCite \textit{R. Duan} et al., J. Math. Phys. 46, No. 5, 053307, 13 p. (2005; Zbl 1110.82034) Full Text: DOI