Global existence for a partially linear 3D Euler flow

Namkwon Kim; Bataa Lkhagvasuren

doi:10.4134/JKMS.j170181

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J. Korean Math. Soc. 2018; 55(1): 211-224

Online first article December 7, 2017 Printed January 1, 2018

https://doi.org/10.4134/JKMS.j170181

Global existence for a partially linear 3D Euler flow

Namkwon Kim, Bataa Lkhagvasuren

Chosun University, Chosun University

Abstract

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Abstract

We consider a certain three dimensional Euler flow with infinite energy, which is sometimes called the columnar or two and half dimensional flow. We prove the global smoothness of such flow in $\mathbb{R}^3$ when the initial data is in some Sobolev or Besov spaces and $\partial_3 u_3$ is nonnegative.

Keywords: columnar flow, incompressible Euler equations, Besov spaces

MSC numbers: Primary 35A01, 35Q35, 35M99