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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
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