Schröder J, Wiedemann E (2026)
Publication Type: Journal article
Publication year: 2026
Book Volume: 33
Article Number: 56
Journal Issue: 2
DOI: 10.1007/s00030-026-01198-z
In this paper we study the vanishing viscosity limit for the inhomogeneous incompressible Navier-Stokes equations on bounded domains with no-slip boundary condition in two or three space dimensions. We show that, under suitable assumptions on the density, we can establish the convergence in energy space of Leray-Hopf type solutions of the Navier-Stokes equation to a smooth solution of the Euler equations if and only if the energy dissipation vanishes on a boundary layer with thickness proportional to the viscosity. This extends Kato’s criterion for homogeneous Navier-Stokes equations to the inhomogeneous case. We use a new relative energy functional in our proof.
APA:
Schröder, J., & Wiedemann, E. (2026). On the vanishing viscosity limit for inhomogeneous incompressible Navier-Stokes equations on bounded domains. Nodea-Nonlinear Differential Equations and Applications, 33(2). https://doi.org/10.1007/s00030-026-01198-z
MLA:
Schröder, Jens, and Emil Wiedemann. "On the vanishing viscosity limit for inhomogeneous incompressible Navier-Stokes equations on bounded domains." Nodea-Nonlinear Differential Equations and Applications 33.2 (2026).
BibTeX: Download