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Global large solutions and incompressible limit for the compressible Navier-Stokes equations. (English) Zbl 1416.35181

Summary: The present paper is dedicated to the global large solutions and incompressible limit for the compressible Navier-Stokes system in \(\mathbb{R}^d\) with \(d\ge 2\). Motivated by the \(L^2\) work of R. Danchin and P. B. Mucha [Adv. Math. 320, 904–925 (2017; Zbl 1384.35058)] in critical Besov spaces, we extend the solution space into an \(L^p\) framework. The result implies the existence of global large solutions initially from large highly oscillating velocity fields.

MSC:

35Q30 Navier-Stokes equations
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35A01 Existence problems for PDEs: global existence, local existence, non-existence

Citations:

Zbl 1384.35058
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References:

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