Time decay rate of solutions to the hyperbolic mhd equations in ℝ3ℝ3

In this paper, we first show the global existence, uniqueness and regularity of weak solutions for the hyperbolic magnetohydrodynamics (MHD) equations in ℝ3ℝ3. Then we establish that the solutions with initial data belonging to Hm(ℝ3)∩L1(ℝ3)Hm(ℝ3)∩L1(ℝ3) have the following time decay rate: ‖m∇u(x,t)‖2+‖m∇b(x,t)‖2+‖∇m+1u(x,t)‖2+‖∇m+1b(x,t)‖2≤c(1+t)-3/2-m‖∇mu(x,t)‖2+‖∇mb(x,t)‖2+‖∇m+1u(x,t)‖2+‖∇m+1b(x,t)‖2≤c(1+t)-3/2-m for large t, where m = 0, 1.