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arXiv · 2507.09333

On 2D Navier-Stokes free boundary: nonnegative density and small viscosity contrast

Francisco Gancedo·Eduardo García-Juárez·Paula Luna-Velasco
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Abstract

This paper is concerned with the evolution of two incompressible, immiscible fluids in two dimensions governed by the inhomogeneous Navier-Stokes equations. We prove global-in-time well-posedness, establishing the preservation of the natural $C^{1+\gamma}$ H\"older regularity of the free boundary, for $0<\gamma<1$. This is the first result that allows for nonnegative density driven by a low-regularity initial velocity, while also remaining valid in the presence of a small viscosity jump.

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Francisco Gancedo, Eduardo García-Juárez, Paula Luna-Velasco. 2025-07-12. On 2D Navier-Stokes free boundary: nonnegative density and small viscosity contrast. https://arxiv.org/abs/2507.09333

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