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A global existence result for the compressible Navier–Stokes equations in the critical \(L ^{p }\) framework. (English) Zbl 1229.35167
The paper investigates the global well-posedness problem for the barotropic compressible Navier-Stokes system in the whole space \({\mathbb{R}}^d\), \(d\geq 2\). Specifically, the case of a critical framework is considered. This critical framework is not related to the energy space. Global existence is obtained for small perturbations of a stable equilibrium state in the sense of suitable \(L^p\)-type Besov norms. Thus one may exhibit a large highly oscillating initial velocity fields for which global well-posedness holds.

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