-
Previous Article
Nonlinear stability of combination of viscous contact wave with rarefaction waves for a 1D radiation hydrodynamics model
- DCDS-B Home
- This Issue
-
Next Article
Kinetic theories for biofilms
Stability of the two dimensional magnetohydrodynamic flows in $\mathbb{R}^3$
1. | Department of Mathematics, Shanghai Finance University, Shanghai 201209 |
2. | Department of Mathematical Sciences, South China Normal University, Guangzhou, 510631 |
References:
[1] |
O. V. Besov, V. P. Il'in and S. M. Nikol'skiĭ, "Integral Representations of Functions, and Imbedding Theorems,", Izdat., (1975).
|
[2] |
L. Caffarelli, R. Kohn and L. Nirenberg, Partial regularity of suitable weak solutions of the Navier-Stokes equations,, Comm. Pure Appl. Math., 35 (1982), 771.
doi: 10.1002/cpa.3160350604. |
[3] |
Chongsheng Cao and Jiahong Wu, Global regularity for the 2D MHD equations with mixed partial dissipation and magnetic diffusion,, Advances in Mathematics, 226 (2011), 1803.
|
[4] |
Cheng He and Zhouping Xin, Partial regularity of suitable weak solutions to the incompressible magnetohydrodynamic equations,, J. Funct. Anal., 227 (2005), 113.
doi: 10.1016/j.jfa.2005.06.009. |
[5] |
Cheng He and Zhouping Xin, On the regularity of weak solutions to the magnetohydrodynamic equations,, J. Differential Equations, 213 (2005), 235.
doi: 10.1016/j.jde.2004.07.002. |
[6] |
G. Duvaut and J.-L. Lions, Inéquations en thermoélasticité et magnétohydrodynamique,, (French) Arch. Rational Mech. Anal., 46 (1972), 241.
|
[7] |
Y. Giga and H. Sohr, Abstract $L^p$ estimates for the Cauchy problem with applications to the Navier-Stokes equations in exterior domains,, J. Funct. Anal., 102 (1991), 72.
doi: 10.1016/0022-1236(91)90136-S. |
[8] |
H. Kozono and Y. Taniuchi, Bilinear estimates in BMO and the Navier-Stokes equations,, Math. Z., 235 (2000), 173.
doi: 10.1007/s002090000130. |
[9] |
Zhen Lei, Global existence of classical solutions for some Oldroyd-B model via the incompressible limit,, Chinese Ann. Math. Ser. B, 27 (2006), 565.
doi: 10.1007/s11401-005-0041-z. |
[10] |
Zhen Lei, On 2D viscoelasticity with small strain,, Arch. Ration. Mech. Anal., 198 (2010), 13.
doi: 10.1007/s00205-010-0346-2. |
[11] |
F.-H. Lin, C. Liu and P. Zhang, On hydrodynamics of viscoelastic fluids,, Comm. Pure Appl. Math., 58 (2005), 1437.
doi: 10.1002/cpa.20074. |
[12] |
Zhen Lei, Chun Liu and Yi Zhou, Global solutions for incompressible viscoelastic fluids,, Arch. Ration. Mech. Anal., 188 (2008), 371.
|
[13] |
Zhen Lei, Chun Liu and Yi Zhou, Global existence for a 2D incompressible viscoelastic model with small strain,, Comm. Math. Sci., 5 (2007), 595.
|
[14] |
Z. Lei and Y. Zhou, BKM's criterion and global weak solutions for magnetohydrodynamics with zero viscosity,, Discrete and Continuous Dynamical Systems, 25 (2009), 575.
doi: 10.3934/dcds.2009.25.575. |
[15] |
Z. Lei and Y. Zhou, Global existence of classical solutions for two-dimensional Oldroyd model via the incompressible limit,, SIAM J. Math. Anal., 37 (2005), 797.
doi: 10.1137/040618813. |
[16] |
Fanghua Lin, A new proof of the Caffarelli-Kohn-Nirenberg theorem,, Comm. Pure Appl. Math., 51 (1998), 241.
doi: 10.1002/(SICI)1097-0312(199803)51:3<241::AID-CPA2>3.0.CO;2-A. |
[17] |
P. B. Mucha, Stability of 2D incompressible flows in $\mathbbR^3$,, J. Differential Equations, 245 (2008), 2355.
doi: 10.1016/j.jde.2008.07.033. |
[18] |
Keyan Wang, On global regularity of incompressible Navier-Stokes equations in $\mathbbR^3$,, Comm. Pure Appl. Anal., 8 (2009), 1067.
doi: 10.3934/cpaa.2009.8.1067. |
[19] |
Jiahong Wu, Regularity results for weak solutions of the 3D MHD equations. Partial differential equations and applications,, Discrete Contin. Dyn. Syst., 10 (2004), 543.
doi: 10.3934/dcds.2004.10.543. |
[20] |
M. Sermange and R. Temam, Some mathematical questions related to the MHD equations,, Comm. Pure Appl. Math., 36 (1983), 635.
doi: 10.1002/cpa.3160360506. |
[21] |
Fan Wang and Keyan Wang, Global regularity for the 3D MHD equations with mixed partial dissipation with small initial data,, preprint., (). Google Scholar |
[22] |
Y. Zhou, Regularity criteria for the generalized viscous MHD equations,, Ann. Inst. H. Poincaré Anal. Non Linéaire, 24 (2007), 491.
|
[23] |
Y. Zhou, Regularity criteria for the 3D MHD equations in terms of the pressure,, Internat. J. Non-Linear Mech., 41 (2006), 1174.
doi: 10.1016/j.ijnonlinmec.2006.12.001. |
[24] |
Y. Zhou, Remarks on regularities for the 3D MHD equations,, Discrete Contin. Dyn. Syst., 12 (2005), 881.
doi: 10.3934/dcds.2005.12.881. |
show all references
References:
[1] |
O. V. Besov, V. P. Il'in and S. M. Nikol'skiĭ, "Integral Representations of Functions, and Imbedding Theorems,", Izdat., (1975).
|
[2] |
L. Caffarelli, R. Kohn and L. Nirenberg, Partial regularity of suitable weak solutions of the Navier-Stokes equations,, Comm. Pure Appl. Math., 35 (1982), 771.
doi: 10.1002/cpa.3160350604. |
[3] |
Chongsheng Cao and Jiahong Wu, Global regularity for the 2D MHD equations with mixed partial dissipation and magnetic diffusion,, Advances in Mathematics, 226 (2011), 1803.
|
[4] |
Cheng He and Zhouping Xin, Partial regularity of suitable weak solutions to the incompressible magnetohydrodynamic equations,, J. Funct. Anal., 227 (2005), 113.
doi: 10.1016/j.jfa.2005.06.009. |
[5] |
Cheng He and Zhouping Xin, On the regularity of weak solutions to the magnetohydrodynamic equations,, J. Differential Equations, 213 (2005), 235.
doi: 10.1016/j.jde.2004.07.002. |
[6] |
G. Duvaut and J.-L. Lions, Inéquations en thermoélasticité et magnétohydrodynamique,, (French) Arch. Rational Mech. Anal., 46 (1972), 241.
|
[7] |
Y. Giga and H. Sohr, Abstract $L^p$ estimates for the Cauchy problem with applications to the Navier-Stokes equations in exterior domains,, J. Funct. Anal., 102 (1991), 72.
doi: 10.1016/0022-1236(91)90136-S. |
[8] |
H. Kozono and Y. Taniuchi, Bilinear estimates in BMO and the Navier-Stokes equations,, Math. Z., 235 (2000), 173.
doi: 10.1007/s002090000130. |
[9] |
Zhen Lei, Global existence of classical solutions for some Oldroyd-B model via the incompressible limit,, Chinese Ann. Math. Ser. B, 27 (2006), 565.
doi: 10.1007/s11401-005-0041-z. |
[10] |
Zhen Lei, On 2D viscoelasticity with small strain,, Arch. Ration. Mech. Anal., 198 (2010), 13.
doi: 10.1007/s00205-010-0346-2. |
[11] |
F.-H. Lin, C. Liu and P. Zhang, On hydrodynamics of viscoelastic fluids,, Comm. Pure Appl. Math., 58 (2005), 1437.
doi: 10.1002/cpa.20074. |
[12] |
Zhen Lei, Chun Liu and Yi Zhou, Global solutions for incompressible viscoelastic fluids,, Arch. Ration. Mech. Anal., 188 (2008), 371.
|
[13] |
Zhen Lei, Chun Liu and Yi Zhou, Global existence for a 2D incompressible viscoelastic model with small strain,, Comm. Math. Sci., 5 (2007), 595.
|
[14] |
Z. Lei and Y. Zhou, BKM's criterion and global weak solutions for magnetohydrodynamics with zero viscosity,, Discrete and Continuous Dynamical Systems, 25 (2009), 575.
doi: 10.3934/dcds.2009.25.575. |
[15] |
Z. Lei and Y. Zhou, Global existence of classical solutions for two-dimensional Oldroyd model via the incompressible limit,, SIAM J. Math. Anal., 37 (2005), 797.
doi: 10.1137/040618813. |
[16] |
Fanghua Lin, A new proof of the Caffarelli-Kohn-Nirenberg theorem,, Comm. Pure Appl. Math., 51 (1998), 241.
doi: 10.1002/(SICI)1097-0312(199803)51:3<241::AID-CPA2>3.0.CO;2-A. |
[17] |
P. B. Mucha, Stability of 2D incompressible flows in $\mathbbR^3$,, J. Differential Equations, 245 (2008), 2355.
doi: 10.1016/j.jde.2008.07.033. |
[18] |
Keyan Wang, On global regularity of incompressible Navier-Stokes equations in $\mathbbR^3$,, Comm. Pure Appl. Anal., 8 (2009), 1067.
doi: 10.3934/cpaa.2009.8.1067. |
[19] |
Jiahong Wu, Regularity results for weak solutions of the 3D MHD equations. Partial differential equations and applications,, Discrete Contin. Dyn. Syst., 10 (2004), 543.
doi: 10.3934/dcds.2004.10.543. |
[20] |
M. Sermange and R. Temam, Some mathematical questions related to the MHD equations,, Comm. Pure Appl. Math., 36 (1983), 635.
doi: 10.1002/cpa.3160360506. |
[21] |
Fan Wang and Keyan Wang, Global regularity for the 3D MHD equations with mixed partial dissipation with small initial data,, preprint., (). Google Scholar |
[22] |
Y. Zhou, Regularity criteria for the generalized viscous MHD equations,, Ann. Inst. H. Poincaré Anal. Non Linéaire, 24 (2007), 491.
|
[23] |
Y. Zhou, Regularity criteria for the 3D MHD equations in terms of the pressure,, Internat. J. Non-Linear Mech., 41 (2006), 1174.
doi: 10.1016/j.ijnonlinmec.2006.12.001. |
[24] |
Y. Zhou, Remarks on regularities for the 3D MHD equations,, Discrete Contin. Dyn. Syst., 12 (2005), 881.
doi: 10.3934/dcds.2005.12.881. |
[1] |
José Luiz Boldrini, Jonathan Bravo-Olivares, Eduardo Notte-Cuello, Marko A. Rojas-Medar. Asymptotic behavior of weak and strong solutions of the magnetohydrodynamic equations. Electronic Research Archive, 2021, 29 (1) : 1783-1801. doi: 10.3934/era.2020091 |
[2] |
Yang Liu. Global existence and exponential decay of strong solutions to the cauchy problem of 3D density-dependent Navier-Stokes equations with vacuum. Discrete & Continuous Dynamical Systems - B, 2021, 26 (3) : 1291-1303. doi: 10.3934/dcdsb.2020163 |
[3] |
Xiaoping Zhai, Yongsheng Li. Global large solutions and optimal time-decay estimates to the Korteweg system. Discrete & Continuous Dynamical Systems - A, 2021, 41 (3) : 1387-1413. doi: 10.3934/dcds.2020322 |
[4] |
Ting Liu, Guo-Bao Zhang. Global stability of traveling waves for a spatially discrete diffusion system with time delay. Electronic Research Archive, , () : -. doi: 10.3934/era.2021003 |
[5] |
Qing Li, Yaping Wu. Existence and instability of some nontrivial steady states for the SKT competition model with large cross diffusion. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3657-3682. doi: 10.3934/dcds.2020051 |
[6] |
Pierre Baras. A generalization of a criterion for the existence of solutions to semilinear elliptic equations. Discrete & Continuous Dynamical Systems - S, 2021, 14 (2) : 465-504. doi: 10.3934/dcdss.2020439 |
[7] |
Stefan Ruschel, Serhiy Yanchuk. The spectrum of delay differential equations with multiple hierarchical large delays. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 151-175. doi: 10.3934/dcdss.2020321 |
[8] |
Junyong Eom, Kazuhiro Ishige. Large time behavior of ODE type solutions to nonlinear diffusion equations. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3395-3409. doi: 10.3934/dcds.2019229 |
[9] |
Izumi Takagi, Conghui Zhang. Existence and stability of patterns in a reaction-diffusion-ODE system with hysteresis in non-uniform media. Discrete & Continuous Dynamical Systems - A, 2020 doi: 10.3934/dcds.2020400 |
[10] |
Ziang Long, Penghang Yin, Jack Xin. Global convergence and geometric characterization of slow to fast weight evolution in neural network training for classifying linearly non-separable data. Inverse Problems & Imaging, 2021, 15 (1) : 41-62. doi: 10.3934/ipi.2020077 |
[11] |
Ahmad Z. Fino, Wenhui Chen. A global existence result for two-dimensional semilinear strongly damped wave equation with mixed nonlinearity in an exterior domain. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5387-5411. doi: 10.3934/cpaa.2020243 |
[12] |
Karoline Disser. Global existence and uniqueness for a volume-surface reaction-nonlinear-diffusion system. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 321-330. doi: 10.3934/dcdss.2020326 |
[13] |
Wenbin Lv, Qingyuan Wang. Global existence for a class of Keller-Segel models with signal-dependent motility and general logistic term. Evolution Equations & Control Theory, 2021, 10 (1) : 25-36. doi: 10.3934/eect.2020040 |
[14] |
Zheng Han, Daoyuan Fang. Almost global existence for the Klein-Gordon equation with the Kirchhoff-type nonlinearity. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020287 |
[15] |
Xing Wu, Keqin Su. Global existence and optimal decay rate of solutions to hyperbolic chemotaxis system in Besov spaces. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2021002 |
[16] |
Vandana Sharma. Global existence and uniform estimates of solutions to reaction diffusion systems with mass transport type boundary conditions. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021001 |
[17] |
Marion Darbas, Jérémy Heleine, Stephanie Lohrengel. Numerical resolution by the quasi-reversibility method of a data completion problem for Maxwell's equations. Inverse Problems & Imaging, 2020, 14 (6) : 1107-1133. doi: 10.3934/ipi.2020056 |
[18] |
Christian Beck, Lukas Gonon, Martin Hutzenthaler, Arnulf Jentzen. On existence and uniqueness properties for solutions of stochastic fixed point equations. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020320 |
[19] |
Tuoc Phan, Grozdena Todorova, Borislav Yordanov. Existence uniqueness and regularity theory for elliptic equations with complex-valued potentials. Discrete & Continuous Dynamical Systems - A, 2021, 41 (3) : 1071-1099. doi: 10.3934/dcds.2020310 |
[20] |
Rim Bourguiba, Rosana Rodríguez-López. Existence results for fractional differential equations in presence of upper and lower solutions. Discrete & Continuous Dynamical Systems - B, 2021, 26 (3) : 1723-1747. doi: 10.3934/dcdsb.2020180 |
2019 Impact Factor: 1.27
Tools
Metrics
Other articles
by authors
[Back to Top]