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Optimal decay rate for strong solutions in critical spaces to the compressible Navier-Stokes equations. (English) Zbl 1300.35080
Summary: In this paper we are concerned with the convergence rates of the global strong solution to motionless state with constant density for the compressible Navier-Stokes equations in the whole space $$\mathbb{R}^n$$ for $$n \geq 3$$. It is proved that the perturbations decay in critical spaces, if the initial perturbations of density and velocity are small in $$B_{2, 1}^{\frac{n}{2}}(\mathbb{R}^n) \cap \dot{B}_{1, \infty}^0(\mathbb{R}^n)$$ and $$B_{2, 1}^{\frac{n}{2} - 1}(\mathbb{R}^n) \cap \dot{B}_{1, \infty}^0(\mathbb{R}^n)$$, respectively.

##### MSC:
 35Q30 Navier-Stokes equations 76N15 Gas dynamics, general 35D35 Strong solutions to PDEs 35B20 Perturbations in context of PDEs
##### Keywords:
compressible Navier-Stokes equations; convergence rate
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##### References:
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