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- W3200730265 abstract "This paper studies the dynamics of two incompressible immiscible fluids in 2D modeled by the inhomogeneous Navier-Stokes equations. We prove that if initially the viscosity contrast is small then there is global-in-time regularity. This result has been proved recently in [32] for $H^{5/2}$ Sobolev regularity of the interface. Here we provide a new approach which allows to obtain preservation of the natural $C^{1+gamma}$ Holder regularity of the interface for all $0<gamma<1$. Our proof is direct and allows for low Sobolev regularity of the initial velocity without any extra technicality. It uses new quantitative harmonic analysis bounds for $C^{gamma}$ norms of even singular integral operators on characteristic functions of $C^{1+gamma}$ domains [21]." @default.
- W3200730265 created "2021-09-27" @default.
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- W3200730265 date "2023-02-07" @default.
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- W3200730265 title "Global regularity of 2D Navier–Stokes free boundary with small viscosity contrast" @default.
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- W3200730265 doi "https://doi.org/10.4171/aihpc/74" @default.
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