PAICU, Marius; ZHANG, Ping; ZHANG, Zhifei

doi:10.1080/03605302.2013.780079

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PAICU, Marius
Institut de Mathématiques de Bordeaux [IMB]

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

ZHANG, Zhifei
School of Mathematical Sciences, Peking University, 100871, P. R. China

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Communications in Partial Differential Equations. 2013, vol. 38, n° 7, p. 1208-1234

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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.< Réduire

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

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