陈亚金, 鲁力, 王金林. 二维含真空非齐次不可压磁流体方程的爆破准则[J]. 南昌航空大学学报(自然科学版), 2016, 30(3): 12-17. DOI: 10.3969/j.issn.1001-4926.2016.03.003
引用本文: 陈亚金, 鲁力, 王金林. 二维含真空非齐次不可压磁流体方程的爆破准则[J]. 南昌航空大学学报(自然科学版), 2016, 30(3): 12-17. DOI: 10.3969/j.issn.1001-4926.2016.03.003
CHEN Ya-jin, LU Li, WANG Jin-lin. A Blow-up Criterion for the Two-Dimensional Nonhomogeneous Incompressible Magnetohydrodynamic Equations with Vacuum[J]. Journal of nanchang hangkong university(Natural science edition), 2016, 30(3): 12-17. DOI: 10.3969/j.issn.1001-4926.2016.03.003
Citation: CHEN Ya-jin, LU Li, WANG Jin-lin. A Blow-up Criterion for the Two-Dimensional Nonhomogeneous Incompressible Magnetohydrodynamic Equations with Vacuum[J]. Journal of nanchang hangkong university(Natural science edition), 2016, 30(3): 12-17. DOI: 10.3969/j.issn.1001-4926.2016.03.003

二维含真空非齐次不可压磁流体方程的爆破准则

A Blow-up Criterion for the Two-Dimensional Nonhomogeneous Incompressible Magnetohydrodynamic Equations with Vacuum

  • 摘要: 本文建立了初始密度含真空的二维非齐次不可压磁流体方程柯西问题强解的爆破准则,该准则仅与密度有关,而与速度和磁场无关。特别地,本文的结果无需初值满足一定相容性条件,且初值密度允许具有紧支集。

     

    Abstract: This paper establishes a blow-up criterion for strong solutions to the Cauchy problem of the two-dimensional nonhomogeneous incompressible magnetohydrodynamic(MHD) equations with vacuum as far field density. The criterion is only in terms of the spatial weighted density, and is independent of both the velocity and the magnetic field. In particular, the initial data is not imposed any additional compatibility conditions and the initial density can contain vacuum states and even have compact support.

     

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