The paper concerns Cauchy,problem for one-dimensional hydromagnetic dynamics with dissipative terms. When the dissipation coefficient is equal to zero it is shown that the smooth solutions develop shocks in the finite time if the initial amounts of entropy and magnetic field are smaller than those of sound waves; when it is larger than zero, and the initial amounts of entropyI this dissipation coefficient and the magnetic field in each period are smaller than those of sound Waves, then the smooth solutions blow up in the finite time. Moreover, the life-span of the smooth solution is given.
This article is concerned with the existence of maximal attractors in Hi （i = 1, 2, 4） for the compressible Navier-Stokes equations for a polytropic viscous heat conductive ideal gas in bounded annular domains Ωn in Rn（n = 2,3）. One of the important features is that the metric spaces H（1）, H（2）, and H（4） we work with are three incomplete metric spaces, as can be seen from the constraints θ 〉 0 and u 〉 0, with θand u being absolute temperature and specific volume respectively. For any constants δ1, δ2……,δ8 verifying some conditions, a sequence of closed subspaces Hδ（4） H（i） （i = 1, 2, 4） is found, and the existence of maximal （universal） attractors in Hδ（i） （i = 1.2.4） is established.
In this paper, we obtain some global existence results for the higher-dimensionai nonhomogeneous, linear, semilinear and nonlinear thermoviscoelastic systems by using semigroup approach.
The paper concerns with generalized Riemann problem for isentropic flow with dissipation, and show that if the similarity solution to Riemann problem is composed of a backward centered rarefaction wave and a forward centered rarefaction wave, then generalized Riemann problem admits a unique global solution on t≥0. This solution is composed of backward centered wave and a forward centered wave with the origin as their center and then continuous for t 〉0.
