On the locally self-similar singular solutions for the incompressible Euler equations

Liutang Xue

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arXiv · 1410.3054

On the locally self-similar singular solutions for the incompressible Euler equations

Liutang Xue

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Abstract

In this paper we consider the locally backward self-similar solutions for the Euler system, and focus on the case that the possible nontrivial velocity profiles have non-decaying asymptotics. We derive the meaningful representation formula of the pressure profile in terms of velocity profiles in this case, and by using it and the local energy inequality of profiles, we prove some nonexistence results and show the energy behavior concerning the possible velocity profiles.

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Liutang Xue. 2015-02-06. On the locally self-similar singular solutions for the incompressible Euler equations. https://arxiv.org/abs/1410.3054

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