Global Unique Solvability of Inhomogeneous Navier-Stokes Equations with Bounded Density

By Marius Paicu, Ping Zhang, Zhifei Zhang. 2013

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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 u0 ∈ Hs( R 2) for s > 0 in 2-D, or u0 ∈ H1( R 3) satisfying ‖u0‖L2 ‖∇u0‖L2 being sufficiently small in 3-D. This in particular improves the most recent well-posedness result in [10], which requires the initial velocity u0 ∈ H2( 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.

Subfields: Applied Mathematics, Computational Mechanics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a0e938cc54c1821cf82452b95b2623cc3899c8a3