Local in time results for local and non-local capillary Navier-Stokes systems with large dataReport as inadecuate




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1 LAMA - Laboratoire d-Analyse et de Mathématiques Appliquées

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 $\bar{ ho}$ which is not necessarily stable $P-\bar{ ho}$ 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.

Keywords : Besov spaces Local and non-local capillarity Compressible Navier-Stokes system critical spaces





Author: Frederic Charve -

Source: https://hal.archives-ouvertes.fr/



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