HUANG, Jingchi; PAICU, Marius; ZHANG, Ping

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HUANG, Jingchi
Academy of Mathematics and Systems Science [AMSS]

PAICU, Marius
Institut de Mathématiques de Bordeaux [IMB]

ZHANG, Ping
Academy of Mathematics and Systems Science [AMSS]

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Document de travail - Pré-publication

Resumen en inglés

In this paper, we first prove the global existence of weak solutions to the d-dimensional incompressible inhomogeneous Navier-Stokes equations with initial data in critical Besov spaces, which satisfies a non-linear smallness condition. The regularity of the initial velocity is critical to the scaling of this system and is general enough to generate non-Lipschitz velocity field. Furthermore, with additional regularity assumption on the initial velocity or on the initial density, we can also prove the uniqueness of such solution. We should mention that the classical maximal regularity theorem for the heat kernel plays an essential role in this context.< Leer menos

Palabras clave en inglés

Inhomogeneous Navier-Stokes equations

maximal regularity for heat kernel

Littlewood-Paley theory.

Littlewood-Paley theory

Orígen

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Centros de investigación

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251