论文标题
对可压缩3D磁性水力动力学方程的低能弱解的存在和独特性
Existence and uniqueness of low-energy weak solutions to the compressible 3D magnetohydrodynamics equations
论文作者
论文摘要
我们证明了三维可压缩磁性水力学（MHD）方程的弱解的存在和唯一性。我们首先获得具有小$ l^2 $ norm的弱解的存在，该解决方案可能在密度，压力，磁场和速度梯度上表现出一个编码 - 一个不连续性。我们在这里考虑的薄弱解决方案表现出足够的规律性和结构，使我们能够为可压缩的MHD方程发展独特性和连续依赖理论。我们的结果将其推广并扩展到可压缩Navier-Stokes方程的中间弱解。
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.
