论文标题
在$ \ mathbb {r}^d $中的对流扩散方程的混合规范上的下限
Lower bounds on mixing norms for the advection diffusion equation in $\mathbb{R}^d$
论文作者
论文摘要
使用傅立叶分割方法得出了$ \ mathbb {r}^d $ $ \ mathbb {r}^d $中的能量衰减的代数下限。通过猜想在流体中混合的猜想，通过梯度估计和插值获得了溶液反向梯度的$ l^2- $规范的下限。
An algebraic lower bound on the energy decay for solutions of the advection-diffusion equation in $\mathbb{R}^d$ with $d=2,3$ is derived using the Fourier splitting method. Motivated by a conjecture on mixing of passive scalars in fluids, a lower bound on the $L^2-$ norm of the inverse gradient of the solution is obtained via gradient estimates and interpolation.
