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

Raphaël Danchin; Ioann Vasilyev

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

Analysis of PDEs 2023-08-02 v2

Authors: Raphaël Danchin , Ioann Vasilyev

Abstract

In this article, we prove the existence of global solutions to the inhomogeneous incompressible Navier--Stokes equations, whenever the initial velocity belongs to some 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.

Keywords

inhomogeneous incompressible Navier-Stokes equations global solutions BMO^{-1} critical tent spaces variable density

Cite

@article{arxiv.2305.09027,
  title  = {Density-dependent incompressible Navier--Stokes equations in critical tent spaces},
  author = {Raphaël Danchin and Ioann Vasilyev},
  journal= {arXiv preprint arXiv:2305.09027},
  year   = {2023}
}

Comments

Many typos corrected; a few references added

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