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Article Dans Une Revue Communications in Partial Differential Equations Année : 2013

Global unique solvability of inhomogeneous Navier-Stokes equations with bounded density

Résumé

In this paper, we prove the global existence and uniqueness of solution to d-dimensional (for $d=2,3$) incompressible inhomogeneous Navier-Stokes equations with initial density being bounded from above and below by some positive constants, and with initial velocity $u_0\in H^s(\R^2)$ for $s>0$ in 2-D, or $u_0\in H^1(\R^3)$ satisfying $\|u_0\|_{L^2}\|\nabla u_0\|_{L^2}$ being sufficiently small in 3-D. This in particular improves the most recent well-posedness result in [10], which requires the initial velocity $u_0\in H^2(\R^d)$ for the local well-posedness result, and a smallness condition on the fluctuation of the initial density for the global well-posedness result.

Dates et versions

hal-00994640 , version 1 (21-05-2014)

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Marius Paicu, Ping Zhang, Zhifei Zhang. Global unique solvability of inhomogeneous Navier-Stokes equations with bounded density. Communications in Partial Differential Equations, 2013, 38 (7), pp.1208-1234. ⟨10.1080/03605302.2013.780079⟩. ⟨hal-00994640⟩
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