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January/February 2013 Solution formula for the vorticity equations in the half plane with application to high vorticity creation at zero viscosity limit
Yasunori Maekawa
Adv. Differential Equations 18(1/2): 101-146 (January/February 2013). DOI: 10.57262/ade/1355867483

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.

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Yasunori Maekawa. "Solution formula for the vorticity equations in the half plane with application to high vorticity creation at zero viscosity limit." Adv. Differential Equations 18 (1/2) 101 - 146, January/February 2013. https://doi.org/10.57262/ade/1355867483

Information

Published: January/February 2013
First available in Project Euclid: 18 December 2012

zbMATH: 1261.35111
MathSciNet: MR3052712
Digital Object Identifier: 10.57262/ade/1355867483

Subjects:
Primary: 35Q30 , 76D05 , 76D10

Rights: Copyright © 2013 Khayyam Publishing, Inc.

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Vol.18 • No. 1/2 • January/February 2013
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