Abstract
In this paper, we consider the large time behavior of the strong solutions to the three dimensional compressible viscoelastic flows with damping. Based on the energy method and spectral analysis, we analyze the influences of the damping on the global existence and decay rates of compressible viscoelastic flows under some small assumptions in H3-framework. Compared with the time decay rates of solutions to the compressible viscoelastic flows in [1], our results imply that the friction of the damping is stronger than the dissipation effect of the viscosities.
Highlights
In this paper, we are interested in three-dimensional compressible viscoelastic flows with damping in the following form: ( ) t +( ρu) = 0, div + ∇P ( ρ ) −μ∆u λ= + μ ) ∇divu α div ρ FF T − ρu, (1.1)
Based on the energy method and spectral analysis, we analyze the influences of the damping on the global existence and decay rates of compressible viscoelastic flows under some small assumptions in H3-framework
Compared with the time decay rates of solutions to the compressible viscoelastic flows in [1], our results imply that the friction of the damping is stronger than the dissipation effect of the viscosities
Summary
We are interested in three-dimensional compressible viscoelastic flows with damping in the following form:. When the damping term is absence in the system (1), there are many results about the global existence of solution to the compressible viscoelastic flows, refer to [5] [6] [7]. For the Navier-Stokes equations with the electric potential, Wang in [11] proved the global existence of strong solution We consider the global existence and L2-norm decay rates of the compressible viscoelastic flows with the term for β = 1 in H3 framework. We use the standard energy method to prove the global existence under the condition that the initial data are close to the constant equilibrium state.
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