Abstract We prove the existence and uniqueness of weak solutions of the three dimensional compressible magnetohydrodynamics (MHD) equations. We first obtain the existence of weak solutions with small L 2 -norm which may display codimension-one discontinuities in density, pressure, magnetic field and velocity gradient. The weak solutions we consider here exhibit just enough regularity and structure which allow us to develop uniqueness and continuous dependence theory for the compressible MHD equations. Our results generalise and extend those for the intermediate weak solutions of compressible Navier-Stokes equations.

中文翻译：

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可压缩3D磁流体动力学方程低能弱解的存在性和唯一性

摘要 我们证明了三维可压缩磁流体力学(MHD)方程弱解的存在唯一性。我们首先获得了具有小L 2 -范数的弱解的存在性，该弱解可能在密度、压力、磁场和速度梯度方面显示出一维一不连续性。我们在这里考虑的弱解表现出足够的规律性和结构，这使我们能够为可压缩 MHD 方程开发唯一性和连续依赖理论。我们的结果推广和扩展了可压缩 Navier-Stokes 方程的中间弱解的结果。