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

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.

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

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