# Boundary Vorticity Estimates for Navier-Stokes and Application to the Inviscid Limit

@inproceedings{Vasseur2021BoundaryVE, title={Boundary Vorticity Estimates for Navier-Stokes and Application to the Inviscid Limit}, author={Alexis Vasseur and Jincheng Yang}, year={2021} }

Consider the steady solution to the incompressible Euler equation ū = Ae1 in the periodic tunnel Ω = Td−1 × (0, 1) in dimension d = 2, 3. Consider now the family of solutions uν to the associated Navier-Stokes equation with the no-slip condition on the flat boundaries, for small viscosities ν = A/Re, and initial values in L2. We are interested in the weak inviscid limits up to subsequences uν ⇀ u∞ when both the viscosity ν converges to 0, and the initial value u0 converges to Ae1 in L 2. Under…

## References

SHOWING 1-10 OF 52 REFERENCES

On the zero-viscosity limit of the Navier–Stokes equations in R+3 without analyticity

- Mathematics
- 2017

Abstract We consider the zero viscosity limit of the incompressible Navier–Stokes equations with non-slip boundary condition in R + 3 for the initial vorticity located away from the boundary. Unlike…

A Kato type theorem on zero viscosity limit of Navier-Stokes flows

- Mathematics
- 2001

We present a necessary and sufficient condition for the convergence of solutions of the incompressible Navier-Stokes equations to that of the Euler equations at vanishing viscosity. Roughly speaking…

Remarks on Zero Viscosity Limit for Nonstationary Navier- Stokes Flows with Boundary

- Mathematics
- 1984

This paper is concerned with the question of convergence of the nonstationary, incompressible Navier-Stokes flow u = u v to the Euler flow u as the viscosity v tends to zero. If the underlying space…

Observations on the vanishing viscosity limit

- Mathematics, Physics
- 2014

Whether, in the presence of a boundary, solutions of the Navier-Stokes equations converge to a solution to the Euler equations in the vanishing viscosity limit is unknown. In a seminal 1983 paper,…

On Kato's conditions for vanishing viscosity

- Mathematics
- 2007

Let u be a solution to the Navier-Stokes equations with viscosity v in a bounded domain Q in R d , d > 2, and let Ū be the solution to the Euler equations in Q. In 1983 Tosio Kato showed that for…

Remarks on the Inviscid Limit for the Navier-Stokes Equations for Uniformly Bounded Velocity Fields

- Mathematics, Computer ScienceSIAM J. Math. Anal.
- 2017

It is proved that the inviscid limit holds in the energy norm if the product of the components of the Navier-Stokes solutions are equicontinuous at $x_2=0$.

Uniqueness and stability of entropy shocks to the isentropic Euler system in a class of inviscid limits from a large family of Navier–Stokes systems

- Mathematics
- 2019

We prove the uniqueness and stability of entropy shocks to the isentropic Euler systems among all vanishing viscosity limits of solutions to associated Navier-Stokes systems. To take into account the…

Vanishing viscosity plane parallel channel flow and related singular perturbation problems

- Mathematics
- 2008

We study a special class of solutions to the 3D Navier-Stokes equations ∂tu +∇uνu +∇p = ν∆u , with no-slip boundary condition, on a domain of the form Ω = {(x, y, z) : 0 ≤ z ≤ 1}, dealing with…

Estimates on fractional higher derivatives of weak solutions for the Navier–Stokes equations

- Mathematics
- 2011

We study weak solutions of the 3D Navier-Stokes equations in whole space with L 2 initial data. It will be proved that r u is locally integrable in space-time for any real such that 1 < < 3, which…

Second Derivatives Estimate of Suitable Solutions to the 3D Navier–Stokes Equations

- Mathematics, Physics
- 2020

We study the second spatial derivatives of suitable weak solutions to the incompressible Navier-Stokes equations in dimension three. We show that it is locally $L ^{\frac43, q}$ for any $q >…