American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Existence and uniqueness of positive solutions for singular biharmonic elliptic systems
  • PROC Home
  • This Issue
  • Next Article
    Global existence and low Mach number limit to the 3D compressible magnetohydrodynamic equations in a bounded domain
2015, 2015(special): 395-399. doi: 10.3934/proc.2015.0395

A regularity criterion for 3D density-dependent MHD system with zero viscosity

Jishan Fan 1, and  Tohru Ozawa 2,

1. 

Department of Applied Mathematics, Nanjing Forestry University, Nanjing, 210037
2. 

Department of Applied Physics, Waseda University, Tokyo, 169-8555

Received  September 2014 Revised  November 2014 Published  November 2015

This paper proves a regularity criterion $\nabla u,\nabla b\in L^\infty(0,T;L^\infty)$ for 3D density-dependent MHD system with zero viscosity and positive initial density.
Keywords: MHD, ideal fluid., regularity criterion.
Mathematics Subject Classification: 35Q30, 76D03, 76D0.
Citation: Jishan Fan, Tohru Ozawa. A regularity criterion for 3D density-dependent MHD system with zero viscosity. Conference Publications, 2015, 2015 (special) : 395-399. doi: 10.3934/proc.2015.0395
References:
[1]

H. Abidi, M. Paicu, Global existence for the magnetohydrodynamic system in critical spaces., Proc. Roy. Soc. Edinburgh Sect. A 138(3)(2008) 447-476., (2008), 447.   Google Scholar

[2]

J. Fan, F. Li, G. Nakamura, Z. Tan, Regularity criteria for the three-dimensional magnetohydrodynamic equations., J. Diff. Equ. 256(2014) 2858-2875., (2014), 2858.   Google Scholar

[3]

J. Fan, Y. Zhou, Uniform local well-posedness for the density-dependent magnetohydrodynamic equations., Appl. Math. Lett. 24(11)(2011) 1945-1949., (2011), 1945.   Google Scholar

[4]

D. Chae, J. Lee, Local existence and blow-up criterion of the inhomogeneous Euler equations., J. Math. Fluid Mech. 5(2003) 144-165., (2003), 144.   Google Scholar

[5]

T. Kato, G. Ponce, Commutator estimates and the Euler and the Navier-Stokes equations., Comm. Pure Appl. Math. 41(1988) 891-907., (1988), 891.   Google Scholar

show all references

References:
[1]

H. Abidi, M. Paicu, Global existence for the magnetohydrodynamic system in critical spaces., Proc. Roy. Soc. Edinburgh Sect. A 138(3)(2008) 447-476., (2008), 447.   Google Scholar

[2]

J. Fan, F. Li, G. Nakamura, Z. Tan, Regularity criteria for the three-dimensional magnetohydrodynamic equations., J. Diff. Equ. 256(2014) 2858-2875., (2014), 2858.   Google Scholar

[3]

J. Fan, Y. Zhou, Uniform local well-posedness for the density-dependent magnetohydrodynamic equations., Appl. Math. Lett. 24(11)(2011) 1945-1949., (2011), 1945.   Google Scholar

[4]

D. Chae, J. Lee, Local existence and blow-up criterion of the inhomogeneous Euler equations., J. Math. Fluid Mech. 5(2003) 144-165., (2003), 144.   Google Scholar

[5]

T. Kato, G. Ponce, Commutator estimates and the Euler and the Navier-Stokes equations., Comm. Pure Appl. Math. 41(1988) 891-907., (1988), 891.   Google Scholar

[1]

Feng Cheng, Chao-Jiang Xu. On the Gevrey regularity of solutions to the 3D ideal MHD equations. Discrete & Continuous Dynamical Systems - A, 2019, 39 (11) : 6485-6506. doi: 10.3934/dcds.2019281
[2]

Sadek Gala. A new regularity criterion for the 3D MHD equations in $R^3$. Communications on Pure & Applied Analysis, 2012, 11 (3) : 973-980. doi: 10.3934/cpaa.2012.11.973
[3]

Ming Lu, Yi Du, Zheng-An Yao, Zujin Zhang. A blow-up criterion for the 3D compressible MHD equations. Communications on Pure & Applied Analysis, 2012, 11 (3) : 1167-1183. doi: 10.3934/cpaa.2012.11.1167
[4]

Jishan Fan, Tohru Ozawa. Global Cauchy problem of an ideal density-dependent MHD-$\alpha$ model. Conference Publications, 2011, 2011 (Special) : 400-409. doi: 10.3934/proc.2011.2011.400
[5]

Jiahong Wu. Regularity results for weak solutions of the 3D MHD equations. Discrete & Continuous Dynamical Systems - A, 2004, 10 (1&2) : 543-556. doi: 10.3934/dcds.2004.10.543
[6]

Tomoyuki Suzuki. Regularity criteria in weak spaces in terms of the pressure to the MHD equations. Conference Publications, 2011, 2011 (Special) : 1335-1343. doi: 10.3934/proc.2011.2011.1335
[7]

Xuanji Jia, Yong Zhou. Regularity criteria for the 3D MHD equations via partial derivatives. Kinetic & Related Models, 2012, 5 (3) : 505-516. doi: 10.3934/krm.2012.5.505
[8]

Zhengguang Guo, Sadek Gala. Regularity criterion of the Newton-Boussinesq equations in $R^3$. Communications on Pure & Applied Analysis, 2012, 11 (2) : 443-451. doi: 10.3934/cpaa.2012.11.443
[9]

Xuanji Jia, Zaihong Jiang. An anisotropic regularity criterion for the 3D Navier-Stokes equations. Communications on Pure & Applied Analysis, 2013, 12 (3) : 1299-1306. doi: 10.3934/cpaa.2013.12.1299
[10]

Kashif Ali Abro, Ilyas Khan. MHD flow of fractional Newtonian fluid embedded in a porous medium via Atangana-Baleanu fractional derivatives. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 377-387. doi: 10.3934/dcdss.2020021
[11]

Xuanji Jia, Yong Zhou. Regularity criteria for the 3D MHD equations via partial derivatives. II. Kinetic & Related Models, 2014, 7 (2) : 291-304. doi: 10.3934/krm.2014.7.291
[12]

Jishan Fan, Tohru Ozawa. Regularity criteria for the magnetohydrodynamic equations with partial viscous terms and the Leray-$\alpha$-MHD model. Kinetic & Related Models, 2009, 2 (2) : 293-305. doi: 10.3934/krm.2009.2.293
[13]

Quansen Jiu, Jitao Liu. Global regularity for the 3D axisymmetric MHD Equations with horizontal dissipation and vertical magnetic diffusion. Discrete & Continuous Dynamical Systems - A, 2015, 35 (1) : 301-322. doi: 10.3934/dcds.2015.35.301
[14]

Jishan Fan, Tohru Ozawa. Regularity criteria for the 2D MHD system with horizontal dissipation and horizontal magnetic diffusion. Kinetic & Related Models, 2014, 7 (1) : 45-56. doi: 10.3934/krm.2014.7.45
[15]

Francesca Bucci, Irena Lasiecka. Regularity of boundary traces for a fluid-solid interaction model. Discrete & Continuous Dynamical Systems - S, 2011, 4 (3) : 505-521. doi: 10.3934/dcdss.2011.4.505
[16]

Daoyuan Fang, Chenyin Qian. Regularity criterion for 3D Navier-Stokes equations in Besov spaces. Communications on Pure & Applied Analysis, 2014, 13 (2) : 585-603. doi: 10.3934/cpaa.2014.13.585
[17]

Zujin Zhang. A Serrin-type regularity criterion for the Navier-Stokes equations via one velocity component. Communications on Pure & Applied Analysis, 2013, 12 (1) : 117-124. doi: 10.3934/cpaa.2013.12.117
[18]

Jishan Fan, Fucai Li, Gen Nakamura. A regularity criterion for the 3D full compressible magnetohydrodynamic equations with zero heat conductivity. Discrete & Continuous Dynamical Systems - B, 2018, 23 (4) : 1757-1766. doi: 10.3934/dcdsb.2018079
[19]

Luigi C. Berselli, Jishan Fan. Logarithmic and improved regularity criteria for the 3D nematic liquid crystals models, Boussinesq system, and MHD equations in a bounded domain. Communications on Pure & Applied Analysis, 2015, 14 (2) : 637-655. doi: 10.3934/cpaa.2015.14.637
[20]

Simon Castle, Norbert Peyerimhoff, Karl Friedrich Siburg. Billiards in ideal hyperbolic polygons. Discrete & Continuous Dynamical Systems - A, 2011, 29 (3) : 893-908. doi: 10.3934/dcds.2011.29.893

 Impact Factor: 

Tools

Metrics

  • PDF downloads (36)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences