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

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2015, 2015(special): 395-399. doi: 10.3934/proc.2015.0395

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

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

Abstract
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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
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[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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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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