三维有界域上不可压缩无磁耗散MHD方程弱解的能量守恒

Energy Conservation for the Weak Solutions to the Three-Dimensional Incompressible Magnetohydrodynamic Equations of Viscous Non-Resistive Fluids in a Bounded Domain

摘要: 本文研究了三维有界域上不可压缩无磁耗散MHD方程弱解的能量守恒问题.先对方程进行整体磨光, 再取截断函数, 然后关于δ，ε，τ取极限,从而得到能量等式.为了得到能量守恒,对弱解(u,b,P)加条件:u∈L_t^pL_x^q,b∈L_t⁴L_x⁴且∇b∈L_t²L_x²,P∈L_t²L_x².

Abstract: In this paper, we mainly study the energy conservation for the weak solutions to the three-dimensional incompressible magnetohydrodynamic equations of viscous non- resistive fluids in a bounded domain. To get energy conservation, we first use the global mollification method to the equation, next take cut-off function, then get the limit of δ,ε,τ. We propose a condition for (u,b,P): u∈L_t^pL_x^q,b∈L_t⁴L_x⁴且∇b∈L_t²L_x²,P∈L_t²L_x².