In this paper, we first show the global existence, uniqueness and regularity of weak solutions for the hyperbolic magnetohydrodynamics(MHD) equations in R^3. Then we establish that the solutions with initial data belonging to H^m(R^3) ∩ L^1(R^3) have the following time decay rate:║▽~mu(x, t) ║~2+║▽~mb(x, t)║~ 2+ ║▽^(m+1)u(x, t)║~ 2+ ║▽^(m+1)b(x, t) ║~2≤ c(1 + t)^(-3/2-m)for large t, where m = 0, 1.
This paper studies the trajectory asymptotic behavior of a non-autonomous incompressible non-Newtonian fluid in 3 D bounded domains. In appropriate topologies, the authors prove the existence of the uniform trajectory attractor for the translation semigroup acting on the united trajectory space.
This paper discusses the relation between the long-time dynamics of solutions of the two-dimensional(2D) incompressible non-Newtonian fluid system and the 2D Navier-Stokes system.We first show that the solutions of the non-Newtonian fluid system converge to the solutions of the Navier-Stokes system in the energy norm.Then we establish that the global attractors {AHε} 0<ε≤1 of the non-Newtonian fluid system converge to the global attractor AH0 of the Navier-Stokes system as → 0.We also construct the minimal limit AHmin of the global attractors {AHε}0<ε≤1 as ε→ 0 and prove that AHmin is a strictly invariant and connected set.
