Global smooth solutions to the 2-D inhomogeneous Navier-Stokes equations with variable viscosity

Abstract

Under the assumptions that the initial density ρ ₀ is close enough to 1 and ρ ₀ − 1 ∈ H ^s+1(ℝ²), u ₀ ∈ H ^s(ℝ²) ∩ Ḣ^−ε(ℝ²) for s > 2 and 0 < ε < 1, the authors prove the global existence and uniqueness of smooth solutions to the 2-D inhomogeneous Navier-Stokes equations with the viscous coefficient depending on the density of the fluid. Furthermore, the L ² decay rate of the velocity field is obtained.

Keywords

Inhomogeneous Navier-Stokes equations / Littlewood-Paley theory / Global smooth solutions

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