Global existence and convergence of nondimensionalized incompressible Navier-Stokes equations in low Froude number regime

Stefano Scrobogna

doi:10.3934/dcds.2020235

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2020, Volume 40, Issue 9: 5471-5511. Doi: 10.3934/dcds.2020235

This issue Previous Article Multiplicity of solutions for critical quasilinear Schrödinger equations using a linking structure Next Article Nonexistence of global solutions for the semilinear Moore – Gibson – Thompson equation in the conservative case

Global existence and convergence of nondimensionalized incompressible Navier-Stokes equations in low Froude number regime

Stefano Scrobogna

IMUS & Departamento de Análisis Matemático, Universidad de Sevilla, C/Tarfia s/n, Campus Reina Mercedes, 41012 Sevilla, Spain

Received: December 2019

Revised: March 2020

Published: June 2020

This research is supported by the Basque Government through the BERC 2018-2021 program and by Spanish Ministry of Economy and Competitiveness MINECO through BCAM Severo Ochoa excellence accreditation SEV-2017-0718 and through project MTM2017-82184-R funded by (AEI/FEDER, UE) and acronym DESFLU and by the European Research Council through the Starting Grant project H2020-EU.1.1.-639227 FLUID INTERFACE

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We prove that the incompressible, density dependent, Navier-Stokes equations are globally well posed in a low Froude number regime. The density profile is supposed to be increasing in depth and linearized around a stable state. Moreover if the Froude number tends to zero we prove that such system converges (strongly) to a two-dimensional, stratified Navier-Stokes equations with full diffusivity. No smallness assumption is considered on the initial data.

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Mathematics Subject Classification: Primary: 35B25, 76D03; Secondary: 76D33.

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