# 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

#### One Citation

Quantitative H\"older Estimates for Even Singular Integral Operators on Patches

- Mathematics
- 2021

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 of… Expand

#### References

SHOWING 1-10 OF 41 REFERENCES

Global Unique Solvability of Inhomogeneous Navier-Stokes Equations with Bounded Density

- Physics, Mathematics
- 2013

In this paper, we prove the global existence and uniqueness of solution to d-dimensional (for d = 2, 3) incompressible inhomogeneous Navier-Stokes equations with initial density being bounded from… Expand

The Incompressible Navier‐Stokes Equations in Vacuum

- Mathematics
- Communications on Pure and Applied Mathematics
- 2018

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. In… Expand

A Lagrangian Approach for the Incompressible Navier-Stokes Equations with Variable Density

- Mathematics
- 2011

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-time… Expand

Striated Regularity of 2-D Inhomogeneous Incompressible Navier–Stokes System with Variable Viscosity

- 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 and… Expand

Incompressible Flows with Piecewise Constant Density

- Mathematics
- 2013

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

Global Regularity of 2D Density Patches for Inhomogeneous Navier–Stokes

- Physics, Mathematics
- 2016

This paper is about Lions’ open problem on density patches (Lions in Mathematical topics in fluid mechanics. Vol. 1, volume 3 of Oxford Lecture series in mathematics and its applications, Clarendon… Expand

On the persistence of Hölder regular patches of density for the inhomogeneous Navier-Stokes equations

- Mathematics
- 2017

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\"older… Expand

Global regularity of three-dimensional density patches for inhomogeneous incompressible viscous flow

- Mathematics, Physics
- Science China Mathematics
- 2018

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 for… Expand

Large time existence of small viscous surface waves without surface tension

- Mathematics
- 1990

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 a… Expand

Regularity Results for Two-Dimensional Flows of Multiphase Viscous Fluids

- Mathematics
- 1997

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 without… Expand