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Global existence and optimal decay rate for the strong solutions in \(H^{2}\) to the compressible Navier-Stokes equations. (English) Zbl 1398.76194
Summary: We prove the global existence of a unique strong solution to the compressible Navier-Stokes equations when the initial perturbation is small in \(H^{2}\). If further that the \(L^{1}\) norm of initial perturbation is finite, we prove the optimal \(L^{2}\) decay rates for such a solution and its first-order spatial derivatives.

MSC:
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35Q30 Navier-Stokes equations
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