Global unique solvability of inhomogeneous incompressible Navier–Stokes equations with nonnegative density

In this paper, we consider the initial-boundary value problem to the inhomogeneous incompressible Navier–Stokes equations in Ω ⊂ R 2 . The initial density is allowed to be nonnegative, and in particular, the initial vacuum is allowed. The global existence and uniqueness of solutions are proved, for...

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Bibliographic Details
Published in:Nonlinearity 2022-09, Vol.35 (9), p.4795-4819
Main Authors: Zhang, Jianzhong, Shi, Weixuan, Cao, Hongmei
Format: Article
Language:English
Subjects:
global unique solvability
inhomogeneous Navier–Stokes equations
nonnegative density
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Summary:In this paper, we consider the initial-boundary value problem to the inhomogeneous incompressible Navier–Stokes equations in Ω ⊂ R 2 . The initial density is allowed to be nonnegative, and in particular, the initial vacuum is allowed. The global existence and uniqueness of solutions are proved, for any initial data ( ρ 0 , u 0 ) ∈ L ∞ × H 0 s with s > 0, which constitutes a positive answer to the question raised by Danchin and Mucha (2019 Commun. Pure Appl. Math. 72 1351–85), in which the initial velocity u 0 ∈ H 0 1 (see also Li (2017 J. Differ. Equ. 263 6512–36).
ISSN:0951-7715
1361-6544
DOI:10.1088/1361-6544/ac8042