Corpus ID: 238253039

Global Regularity of 2D Navier-Stokes Free Boundary with Small Viscosity Contrast

@inproceedings{Gancedo2021GlobalRO,
  title={Global Regularity of 2D Navier-Stokes Free Boundary with Small Viscosity Contrast},
  author={Francisco Gancedo and Eduardo Garc{\'i}a-Ju{\'a}rez},
  year={2021}
}
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 H5{2 Sobolev regularity of the interface. Here we provide a new approach which allows to obtain preservation of the natural C1`γ Hölder regularity of the interface for all 0 ă γ ă 1. Our proof is direct and allows for… Expand
Quantitative H\"older Estimates for Even Singular Integral Operators on Patches
Abstract. In this paper we show a constructive method to obtain new Cσ estimates of even singular integral operators on characteristic functions of domains with C regularity, 0 ă σ ă 1. This kind ofExpand

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