Global regularity of 2D density patches for inhomogeneous Navier-Stokes

2016/12/27 by Francisco Gancedo, Gancedo, Francisco, Eduardo García-Juárez +1 · 2 citations
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1612.08665

openalex publication_date 2016/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is about Lions' open problem on density patches \citeLIONS: whether inhomogeneous incompressible Navier-Stokes equations preserve the initial regularity of the free boundary given by density patches. Using classical Sobolev spaces for the velocity, we first establish the propagation of C^1+γ regularity with 0

Citations

• The Viscous Surface-Internal Wave Problem: Global Well-Posedness and Decay
• Almost Exponential Decay of Periodic Viscous Surface Waves without Surface Tension
• Global regularity for 2D Boussinesq temperature patches with no\n diffusion
• On the persistence of Hölder regular patches of density for the inhomogeneous Navier-Stokes equations

Cited by

• On the large time behavior of the 2D inhomogeneous incompressible viscous flows
• On 2D Navier-Stokes free boundary: nonnegative density and small viscosity contrast

Related

• On the density patch problem for the 2-D inhomogeneous Navier-Stokes equations
• Global regularities of two-dimensional density patch for inhomogeneous incompressible viscous flow with general density
• Global regularity of three dimensional density patch for inhomogeneous incompressible viscous flow
• Global regularity of two dimensional inhomogeneous incompressible Navier-Stokes Equations with large data
• On 2D Navier-Stokes free boundary: nonnegative density and small viscosity contrast