Well-posedness of the 2D Euler equations when velocity grows at infinity

Elaine Cozzi; James P. Kelliher

doi:10.3934/dcds.2019100

Article Contents

2019, Volume 39, Issue 5: 2361-2392. Doi: 10.3934/dcds.2019100

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Well-posedness of the 2D Euler equations when velocity grows at infinity

Elaine Cozzi^1, and
James P. Kelliher^2,

1.
Department of Mathematics, 368 Kidder Hall, Oregon State University, Corvallis, OR 97331, USA
2.
Department of Mathematics, University of California, Riverside, USA

Received: September 2017

Revised: September 2018

Published: January 2019

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Abstract

We prove the uniqueness and finite-time existence of bounded-vorticity solutions to the 2D Euler equations having velocity growing slower than the square root of the distance from the origin, obtaining global existence for more slowly growing velocity fields. We also establish continuous dependence on initial data.

Keywords:

Fluid mechanics,
Euler equations.

Mathematics Subject Classification: Primary: 35Q31, 76B03.

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References

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