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On classes of globally smooth solutions to the Euler equations in several dimensions

Olga S. Rozanova
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Abstract

It is shown that if the system of the Euler equations has a special global in time smooth solution with the linear profile of velocity, then another solutions with Cauchy data, close in the Sobolev norm to the initial data of the given solution, will be globally smooth as well. The examples of the solutions are constructed.

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Olga S. Rozanova. 2002-04-03. On classes of globally smooth solutions to the Euler equations in several dimensions. https://arxiv.org/abs/math/0203230

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