Dynamics of Partial Differential Equations
Volume 12 (2015)
On the locally self-similar singular solutions for the incompressible Euler equations
Pages: 321 – 342
In this paper we consider the locally backward self-similar solutions for the Euler system, and specially focus on the case that the possible nontrivial velocity profiles have non-decaying spatial asymptotics. We derive the representation formula of the pressure profile in terms of the velocity profiles in such a situation, and by using it and the local energy inequality of the profiles, we prove some nonexistence results and show the energy behavior concerning these possible velocity profiles.
Euler equations, backward self-similar solutions, nonexistence, energy behavior
2010 Mathematics Subject Classification
35B99, 35L67, 35Q35, 76Bxx