PAICU, Marius; ZHANG, Ping

doi:10.1007/s00220-019-03446-z

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PAICU, Marius
Institut de Mathématiques de Bordeaux [IMB]

ZHANG, Ping
Académie Chinoise des Sciences

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Communications in Mathematical Physics. 2020

Springer Verlag

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2020

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In this paper, we investigate the global existence and uniqueness of strong solutions to 2D incompressible inhomogeneous Navier-Stokes equations with viscous coefficient depending on the density and with initial density being discontinuous across some smooth interface. Compared with the previous results for the inhomogeneous Navier-Stokes equations with constant viscosity, the main difficulty here lies in the fact that the L 1 in time Lipschitz estimate of the velocity field can not be obtained by energy method (see [11, 20, 21] for instance). Motivated by the key idea of Chemin to solve 2-D vortex patch of ideal fluid ([6, 7]), namely, striated regularity can help to get the L ∞ boundedness of the double Riesz transform, we derive the a priori L 1 in time Lipschitz estimate of the velocity field under the assumption that the viscous coefficient is close enough to a positive constant in the bounded function space. As an application, we shall prove the propagation of H 3 regularity of the interface between fluids with different densities.< Réduire

Mots clés en anglais

Inhomogeneous Navier-Stokes equations

Littlewood-Paley theory

Striated regularity

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STRIATED REGULARITY OF 2-D INHOMOGENEOUS INCOMPRESSIBLE NAVIER-STOKES SYSTEM WITH VARIABLE VISCOSITY

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