三维半空间中不可压磁流体力学方程组解的衰减性

Decay Rate of Solutions of Incompressible Magnetohydrodynamics Equations in 3-dimensional Half Space

本文研究三维半空间中不可压磁流体力学方程组弱解的衰减性.当方程满足初始条件(u_0,b_0)∈L^1(R_+~3)∩L^2(R_+~3),(x_3~2u_0,x_3~2b_0)∈L^2(R_+~3),(x_3U_0,x_3b_0)∈L^1(R_+~3)∩L^(6/5)(R_+~3)时,证明了弱解(u(t),b(t))的衰减率为:‖(x_3U(t),x_3b(t))‖L^2(R_+~3)≤c(1+t)^(-5/8),其中c是与t无关的常数.

In this paper we study the L^2 time decay rate of a weak solution of the 3-dimensional incompressible Magnetohydrodynamic equations in the half space. We prove that, for initial value （U0, b0）∈L^1（R＋^3）∩L^2（R＋^3）,（x3^2u0,x3^2b0）∈L^2（R＋^3）,（x3U0,x3b0）∈L^1（R＋^3）∩L（6/5）（R＋^3）,the weak solution satisfying time decay estimates ‖（x3u（t）,x3b（t））‖L^2（R＋^3）≤c（1＋t）^-5/8, for some c independent of t.