论文标题
Leray解决方案的非唯一性在二维中的缺血性Navier-Stokes方程
Non-uniqueness of Leray solutions to the hypodissipative Navier-Stokes equations in two dimensions
论文作者
论文摘要
我们在二维中表现出强制性Navier-Stokes方程的非唯一Leray溶液。与\ cite {albritton2021non}中构建的解决方案不同，我们以超临界缩放构建的解决方案进行了实时，在该缩放中，在这种范围内，在这种缩放范围内，在$ t \ to $ t \ to 0^+$的情况下，缩短降低被正式可忽略不计。在此缩放中，可以将Vishik \ cite {Vishik1，Vishik2}的Euler非唯一性场景扰动到非线性级别的低解剖设置。我们的扰动论点是精神上的学流，并规避了将耗散纳入\ cite {albritton2021non}的频谱理论方法。
We exhibit non-unique Leray solutions of the forced Navier-Stokes equations with hypodissipation in two dimensions. Unlike the solutions constructed in \cite{albritton2021non}, the solutions we construct live at a supercritical scaling, in which the hypodissipation formally becomes negligible as $t \to 0^+$. In this scaling, it is possible to perturb the Euler non-uniqueness scenario of Vishik \cite{Vishik1,Vishik2} to the hypodissipative setting at the nonlinear level. Our perturbation argument is quasilinear in spirit and circumvents the spectral theoretic approach to incorporating the dissipation in \cite{albritton2021non}.
