Optimal time decay rate for compressible viscoelastic equations in critical spaces

Rate of Decay for Solutions of Viscoelastic Evolution Equations

In this article we consider a Cauchy problem of a nonlinear viscoelastic equation of order four. Under suitable conditions on the initial data and the relaxation function, we prove polynomial and logarithmic decay of solutions.

Well-posedness in critical spaces for the compressible Navier-Stokes equations with density dependent viscosities

In this paper, we prove the local well-posedness in critical Besov spaces for the compressible Navier-Stokes equations with density dependent viscosities under the assumption that the initial density is bounded away from zero.

Optimal decay rate of the compressible Navier-Stokes-Poisson system in R

The compressible Navier-Stokes-Poisson (NSP) system is considered in R3 in the present paper and the influences of the electric field of the internal electrostatic potential force governed by the self-consistent Poisson equation on the qualitative behaviors of solutions is analyzed. It is observed that the rotating effect of electric field affects the dispersion of fluids and reduces the time d...

Remark on the Rate of Decay of Solutions to Linearized Compressible Navier-stokes Equations

ρ0 and v0 are given initial data; α and γ are positive constants and β a nonnegative constant. Concerning the decay property, asymptotically, the solution decomposed into sum of two parts under the influence of a hyperbolic aspect and a parabolic aspect. One of which dominates in Lp for 2 p ∞, the other 1 p < 2. For p 2, the time asymptotic behavior of solutions is similar to the solution of pu...

Decay rate of the compressible Navier-Stokes equations with density-dependent viscosity coefficients