Global well-posedness of 3D inhomogenous incompressible Navier-Stokes equations with density-dependent viscosity

2024/01/24 by Dongjuan Niu, Lu Wang, Niu, Dongjuan +1
Mathematics · Engineering · #Navier-Stokes equation solutions #Advanced Mathematical Physics Problems #Computational Fluid Dynamics and Aerodynamics

paper · pdf · doi:10.48550/arxiv.2401.13265

Abstract

The issue of global well-posedness for the 3D inhomogenous incompressible Navier-Stokes equations was first addressed by Kazhikov in 1974. In this manuscript, we obtain its global well-posedness for the system with density-dependent viscosity under the smallness assumption of initial velocity in the critical space B_p,1^{-1+\frac 3p} with p∈ ]1, 9/2]. To the best of our knowledge, this is the first result about the global well-posedness for which one does not assume any smallness condition on the density when the initial density is far away from vacuum.

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