Local in time results for local and non-local capillary Navier-Stokes systems with large data

Abstract

In this article we study three capillary compressible models (the classical local Navier-Stokes-Korteweg system and two non-local models) for large initial data, bounded away from zero, and with a reference pressure state $\bar{\rho }$ which is not necessarily stable ($P^{\prime }(\bar{\rho })$ can be non-positive). We prove that these systems have a unique local in time solution and we study the convergence rate of the solutions of the non-local models towards the local Korteweg model. The results are given for constant viscous coefficients and we explain how to extend them for density dependant coefficients.

arXiv comment39 pages

References in corpus (2)

• Blow-up criterion, ill-posedness and existence of strong solution for Korteweg system with infinite energy
• Existence of solutions for compressible fluid models of Korteweg type