Schedules of future seminars
● 2016 年 7 月 8 日 16:00 〜 18:30
- 京都大学 理学研究科 3 号館 108 号室
Room changed to 108 at Science Building No.3, Kyoto University
- Sanghyuk Lee 氏 （Seoul National University）
Matthew Roy Paddick 氏 （Université Pierre et Marie Curie）
【16:00-17:00 S. Lee】
Uniform Sobolev estimate for 2nd order differential operators
【17:30-18:30 M.R. Paddick】
An existence result for the 2D steady geophysical Prandtl equation
This talk is concerned with the uniform Sobolev type estimate which is independent of the first order and constant terms.
For elliptic operators Lebesgue spaces for which such uniform estimates hold are completely characterized by Kenig, Ruiz, and Sogge.
However, for non-elliptic operators the same problem has been left open until recent.
We answer this problem and also discuss connection to the Fourier restriction estimate and the boundedness of multiplier operators.
We study a viscous boundary layer problem stemming from oceanic motion.
Western currents such as the Gulf Stream or the Kuroshio are formally governed by a Prandtl-like equation in this setting,
and we aim to prove the existence of stationary solutions with positive latitudinal (South-to-North) velocity.
We show that such solutions exist if a set of parameters in the equation is large enough.
These parameters include the profile of the coastline, which gives a clue on the role of the geometry in boundary layer separation.