Long time uniform stability of solutions of magnetohydrodynamics equations (Q1365329)

We study long time uniform stability for solutions to the following two-dimensional magnetohydrodynamics equations \[ \Delta u_t+ J(u,\Delta u)- J(A,\Delta A)- \Delta^2u= 0,\;A_t+ J(u,A)- \Delta A=0, \] \[ u(x,0)= u_0(x),\;A(x,0)= A_0(x), \] where \(x= (x_1,x_2)\in\mathbb{R}^2\), \(t>0\), \(u\), \(A\) are scalar functions of \(x\), \(t\), \(J(a,b)= a_{x_1}b_{x_2}- a_{x_2}b_{x_1}\).