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

2023/05/15 by Raphaël Danchin, Ioann Vasilyev, Danchin, Raphaël +1 · 1 citation
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Compressibility #Computer science #Extension (predicate logic) #Hagen–Poiseuille flow from the Navier–Stokes equations #Mathematical analysis #Mathematics #Mechanics #Metric (unit) #Navier-Stokes equation solutions #Navier–Stokes equations #Physics #Stability and Controllability of Differential Equations #Subspace topology #Variable (mathematics) #math.AP

paper · pdf · doi:10.48550/arxiv.2305.09027

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2023/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

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 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.

Citations

• Some new function spaces and their applications to Harmonic analysis
• Sur le mouvement d'un liquide visqueux emplissant l'espace

Related

• Global solutions to 2-d inhomogeneous navier-stokes system with general velocity
• The incompressible navier-stokes equations in vacuum
• A Lagrangian approach for the incompressible Navier-Stokes equations with variable density
• Inhomogenous Navier--Stokes equations with unbounded density
• On the global existence and uniqueness of solution to 2-D inhomogeneous incompressible Navier-Stokes equations in critical spaces