Seminar| Institute of Mathematical Sciences
Time：Friday, May 7th, 2021, 14:00-15:00
Location：R408, IMS
Speaker: Yuanyuan Feng, The Pennsylvania State University
Abstract: We study the Kuramoto-Sivashinsky equation in scalar form. The analysis of KSE in one space dimension is well developed. In one dimension a priori norm estimates on the solution are closed which lead to a good control on the L2 norm of the solution. In dimension d>1, there is no known global estimate for any Lp norm due to lack of maximum principle. We consider the KSE with linear advection and prove that global existence can be achieved in the presence of growing modes and for arbitrary data, if the advecting field v is relaxation enhancing with sufficiently small dissipation time. We then observe that dissipation enhancement in every direction is not necessary. Global exsitence in two dimension can be achieved by adding some sheear flows and in three dimension can be achieved by adding some so called planar helical flows.