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Renormalization and a-priori bounds for Leray self-similar solutions to the generalized mild Navier-Stokes equations by Gaidashev, Denis is a scholarly article available to read on EtoBox.

What is Renormalization and a-priori bounds for Leray self-similar solutions to the generalized mild Navier-Stokes equations about?

We demonstrate that the problem of existence of Leray self-similar blow up solutions in a generalized mild Navier-Stokes system with the fractional Laplacian $(-\Delta)^{\gamma/2}$ can be stated as a fixed point problem for a "renormalization" operator. We proceed to construct {\it a-priori} bounds, that is a renormalization invariant precompact set in an appropriate weighted $L^p$-space. As a consequence of a-priori bounds, we prove existence of renormalization fixed points for $d \ge 2$ and $d<\gamma <2 d+2$, and existence of non-trivial Leray self-similar mild solutions in $C^\infty([0,T),(H^k)^d \cap (L^p)^d)$, $k>0, p \ge 2$, whose $(L^p)^d$-norm becomes unbounded in finite time $T$.

Author

Gaidashev, Denis

Published

2022

Language

EN