HUANG, Jingchi; PAICU, Marius; ZHANG, Ping

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HUANG, Jingchi
Academy of Mathematics and Systems Science [AMSS]

PAICU, Marius
Institut de Mathématiques de Bordeaux [IMB]

ZHANG, Ping
Academy of Mathematics and Systems Science [AMSS]

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Journal de Mathématiques Pures et Appliquées. 2013, vol. 100, n° 6, p. 806-831

Elsevier

Résumé en anglais

In this paper, we are concerned with the global wellposedness of 2-D density-dependent incompressible Navier-Stokes equations with variable viscosity, in a critical functional frame- work which is invariant by the scaling of the equations and under a non-linear smallness condition on fluctuation of the initial density which has to be doubly exponential small compared with the size of the initial velocity. In the second part of the paper, we apply our methods combined with the techniques of R. Danchin and P. B. Mucha to prove the global existence of solutions to inhomogeneous Navier-Stokes system with piecewise constant initial density which has small jump at the interface and is away from vacuum. In particular, this latter result removes the smallness condition for the initial velocity in a corresponding theorem of R. Danchin and P. B. Mucha.< Réduire

Mots clés en anglais

Inhomogeneous Navier-Stokes Equations

Littlewood-Paley Theory

Wellposedness

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Global Solutions to 2-D Inhomogeneous Navier-Stokes System with General Velocity

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