Corpus ID: 238253039

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

  title={Global Regularity of 2D Navier-Stokes Free Boundary with Small Viscosity Contrast},
  author={Francisco Gancedo and Eduardo Garc{\'i}a-Ju{\'a}rez},
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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We are concerned with the existence and uniqueness issue for the inhomogeneous incompressible Navier-Stokes equations supplemented with H^1 initial velocity and only bounded nonnegative density. InExpand
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We investigate the Cauchy problem for the inhomogeneous Navier-Stokes equations in the whole n-dimensional space. Under some smallness assumption on the data, we show the existence of global-in-timeExpand
Striated Regularity of 2-D Inhomogeneous Incompressible Navier–Stokes System with Variable Viscosity
  • M. Paicu, P. Zhang
  • Physics, Mathematics
  • Communications in Mathematical Physics
  • 2019
In this paper, we investigate the global existence and uniqueness of strong solutions to 2D incompressible inhomogeneous Navier–Stokes equations with viscous coefficient depending on the density andExpand
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We investigate the incompressible Navier–Stokes equations with variable density. The aim is to prove existence and uniqueness results in the case of discontinuous initial density. In dimension n =Expand
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In our recent work dedicated to the Boussinesq equations [Danchin and Zhang 2016], we established the persistence of solutions with piecewise constant temperature along interfaces with H\"olderExpand
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Toward Lions’ open question in Lions (1996) concerning the propagation of regularity for density patch, we prove that the boundary regularity of the 3-D density patch persists by time evolution forExpand
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The motion of a three-dimensional viscous, imcompressible fluid is governed by the Navier-Stokes equations. We study the case where the fluid is in an ocean of infinite extent and finite depth with aExpand
Regularity Results for Two-Dimensional Flows of Multiphase Viscous Fluids
Abstract Global regularity results for weak solutions of the Navier-Stokes equations for two-dimensional multiphase incompressible fluids are proved under suitable conditions on the viscosity withoutExpand