论文标题
Leray自相似解决方案的重新归一化和A-Priori界限
Renormalization and a-priori bounds for Leray self-similar solutions to the generalized mild Navier-Stokes equations
论文作者
论文摘要
我们证明，Leray自相似于溶液的存在问题在具有分数laplacian $（ - δ）^{γ/2} $的广义温和纳维尔 - stokes系统中，可以说是“重新分配”操作员的固定点问题。我们继续构建{\ it A-priori}边界，这是在适当的加权$ l^p $ -space中设置的重新归一化的预发。 由于A-Priori的界限，我们证明存在$ d \ ge 2 $和$ d <γ<2 d+2 $的固定点的存在，并且存在$ c^\ infty（[0，t），（H^K），（H^k）^d \ cap（l^p）$ c^d \ cap（l^p）$ c^\ ge> 0，$ c^\ infty的非客气leray自相似于$（l^p）^d $ -norm在有限的时间$ t $中变得无限。
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 $(-Δ)^{γ/2}$ 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 $d<γ<2 d+2$, 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 $T$.
