an:06350880
Zbl 1300.35080
Okita, Masatoshi
Optimal decay rate for strong solutions in critical spaces to the compressible Navier-Stokes equations
EN
J. Differ. Equations 257, No. 10, 3850-3867 (2014).
00336776
2014
j
35Q30 76N15 35D35 35B20
compressible Navier-Stokes equations; convergence rate
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.