论文标题
线性Sobolev传输中极端的时间间歇性：几乎光滑的非独特解决方案
Extreme temporal intermittency in the linear Sobolev transport: almost smooth nonunique solutions
论文作者
论文摘要
在本文中，我们重新审视了时间间歇性的概念，以获得线性传输方程的尖锐非唯一性结果。我们构建具有尖锐sobolev规则性$ l^1_t w^{1，p} $的无差异矢量字段，用于所有$ p <\ infty $在空间尺寸中的$ d \ geq 2 $，其传输方程允许nonunique nonunique弱解决方案属于所有$ l^p_tc^k $ for of $ l^p_tc^k $ for $ p <\ k k k \ k \ b \ b \ b \ b \ b \ b \ in c \ in。特别是，我们的结果表明，在二翼狮子理论的唯一性中的时间整合性假设很敏锐。对于具有任意大订单的扩散操作员在任何维度上，$ d \ geq 2 $的传输扩散操作员也适用于运输扩散方程。
In this paper, we revisit the notion of temporal intermittency to obtain sharp nonuniqueness results for linear transport equations. We construct divergence-free vector fields with sharp Sobolev regularity $L^1_t W^{1,p}$ for all $p<\infty$ in space dimensions $d\geq 2$ whose transport equations admit nonunique weak solutions belonging to $L^p_tC^k$ for all $p<\infty$ and $k\in \mathbb{N}$. In particular, our result shows that the time-integrability assumption in the uniqueness of the DiPerna-Lions theory is sharp. The same result also holds for transport-diffusion equations with diffusion operators of arbitrarily large order in any dimensions $d \geq 2$.
