Place: Seminario EDP Universidade Federal de Alagoas

Abstract

We prove an exponential lower bound for the ||ρ(x, t)||_{H^{−1}} norm where ρ(x, t) is the solution of the transport equation with a vector field W^{1,p}(T^2) for 2 < p < ∞ and initial data ρ^0 ∈ L^2(T^2). We use the MongeKantorovich-Rubinstein distance as measure.

ICMC Summer Meeting on Differential Equations chapter 2020

http://summer.icmc.usp.br/summers/summer20/download/Summer20.pdf

http://summer.icmc.usp.br/summers/summer19/pg_organizing.php

Place : Seminary EDP UFRJ

Abstract:

We study the problem of exhibit an incompressible flow that mix, in an optimal way a passive scalar. We consider as measures of the degree of mixing, two definitions: The \textit{geometry mixing scale} and the \textit{mixing norm} we provide a motivation and comparison between them. In previous works was shown that the time wasted by an incompressible flow to mix the passive scalar have a logarithmic lower bound. We study a construction of a velocity field given in \cite{yao} that saturate that logarithmic bound. Finally, we will mention some results and open problems that enrich the study of this topic.

Place: VII Oficina de Sistemas Dinâmicos - Universidade Federal de Itajuba