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arXiv · 2305.09027

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

Raphaël Danchin·Ioann Vasilyev
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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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Raphaël Danchin, Ioann Vasilyev. 2023-05-15. Density-dependent incompressible Navier--Stokes equations in critical tent spaces. https://arxiv.org/abs/2305.09027

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