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Between homogeneous and inhomogeneous Navier–Stokes systems: The issue of stability

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Abstract We construct large velocity vector solutions to the three dimensional inhomogeneous Navier–Stokes system. The result is proved via the stability of two dimensional solutions with constant density, under the… Click to show full abstract

Abstract We construct large velocity vector solutions to the three dimensional inhomogeneous Navier–Stokes system. The result is proved via the stability of two dimensional solutions with constant density, under the assumption that initial density is point-wisely close to a constant. Key elements of our approach are estimates in the maximal regularity regime and the Lagrangian coordinates. Considerations are done in the whole R 3 .

Keywords: homogeneous inhomogeneous; stokes systems; inhomogeneous navier; systems issue; stability; navier stokes

Journal Title: Journal of Differential Equations
Year Published: 2019

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