Advances in Differential Equations

Solution formula for the vorticity equations in the half plane with application to high vorticity creation at zero viscosity limit

Yasunori Maekawa

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We consider the Navier--Stokes equations for viscous incompressible flows in the half plane under the no-slip boundary condition. In this paper we first establish a solution formula for the vorticity equations through the appropriate vorticity formulation. The formula is then applied to establish the asymptotic expansion of vorticity fields at $\nu\rightarrow 0$ that holds at least up to the time $c\nu^{1/3}$, where $\nu$ is the viscosity coefficient and $c$ is a constant. As a consequence, we get a natural sufficient condition on the initial data for the vorticity to blow up at the inviscid limit, together with explicit estimates.

Article information

Source
Adv. Differential Equations Volume 18, Number 1/2 (2013), 101-146.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867483

Mathematical Reviews number (MathSciNet)
MR3052712

Zentralblatt MATH identifier
1261.35111

Subjects
Primary: 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10] 76D05: Navier-Stokes equations [See also 35Q30] 76D10: Boundary-layer theory, separation and reattachment, higher-order effects

Citation

Maekawa, Yasunori. Solution formula for the vorticity equations in the half plane with application to high vorticity creation at zero viscosity limit. Adv. Differential Equations 18 (2013), no. 1/2, 101--146. https://projecteuclid.org/euclid.ade/1355867483.


Export citation