可压缩磁流体方程组整体弱解的不存在性

On the nonexistence of global weak solutions to compressible MHD equations

在RN,N≥2中研究了可压缩磁流体方程组整体弱解的不存在性。在密度、速度和磁场满足一定的积分条件下,如果初值满足∫RNρ0(x)v0(x)x/|x|[∫0|x|w(r)dr]dx≥0,那么整体弱解中的密度和磁场都是零解;如果初值满足∫RNρ0(x)v0(x)x/|x|[∫0|x|w(r)dr]dx>0,其中w(r)是[0,∞)上某个正的非增函数,那么可压缩磁流体方程组不存在整体弱解。

The nonexistence of global weak solutions to compressible MHD equations is proved in RN,N≥2.Under suitable assumptions on integrability for the density,velocity and magnetic fields,for some non-increasing function w（r）0,r∈[0,∞）,if the initial datum satisfies ∫RN ρ0（x）v0（x）/x ｜x｜[∫｜x｜0w（r）dr]dx≥0,then the only global weak solutions to the compressible MHD equations correspond to the zero density and the zero magnetic field and if the initial datum satisfies ∫RN ρ0（x）v0（x）x/｜x｜[∫｜x｜0w（r）dr]dx0,then the global weak solutions to the compressible MHD equations do not exist.