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Density-dependent incompressible Navier--Stokes equations in critical tent spaces

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arxiv 2305.09027 v3 pith:R2QDCLSV submitted 2023-05-15 math.AP

Raphaël Danchin , Ioann Vasilyev This is my paper · ORCID
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keywords equationsdensityincompressibleinitialnavier--stokesarticlebelongscase
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abstract

In this article, we prove the existence of global solutions to the inhomogeneous incompressible Navier--Stokes equations, whenever the initial velocity belongs to a certain subspace of $\mathrm{BMO}^{-1}$, and the initial density is sufficiently close to $1$ in the uniform metric. This is a natural extension to the variable density case of the celebrated result by H. Koch and D. Tataru concerning the classical Navier-Stokes equations.

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  1. Global well-posedness and self-similar solution of the inhomogeneous Navier-Stokes system

    math.AP 2024-11 conditional novelty 7.0 of 10

    Global well-posedness is proven for the 3D inhomogeneous Navier-Stokes system with discontinuous density and small velocity in critical Besov spaces, yielding the first forward self-similar solutions.

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