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    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

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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

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