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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
##### Keywords:
energy estimate; uniqueness; small initial perturbation
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##### References:
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