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Optimal convergence rates for the compressible Navier-Stokes equations with potential forces. (English) Zbl 1122.35093
The authors consider the motion of compressible viscous and heat-conductive fluids in the whole space \(\mathbb R^2\). This is described mathematically by a initial boundary value problem of the compressible Navier-Stokes equations for the density, the velocity, and the temperature. In the considered case, the Navier-Stokes equation contains an external potential force term. Based on \(L^p\)-\(L^q\) estimates for the linearized equations and an energy method, optimal convergence rates in various Sobolev norms for the solution to the stationary profile are proved. It is supposed that the initial perturbation of the stationary solution and the potential force are small in some Sobolev norms.

MSC:
35Q30 Navier-Stokes equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
93D20 Asymptotic stability in control theory
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