Program
⾮线性⾊散⽅程:确定性和概率⽅法
Student No.:50
Time:Tue/Thu 13:00-14:50, 2016-07-26 ~ 2016-08-25
Instructor:Yu Deng  [Courant Institute of Mathematical Sciences ]
Place:Conference room 4, floor 2, Jin Chun Yuan West Building
Starting Date:2016-7-26
Ending Date:2016-8-25
 

 

Description:

 

 

 

课程分为两部分,第部分讲述线性和线性程的基本理论。第部分中我们会介绍最近20年中发展的重要法和技巧,包括:X^{s,b}空间理论,数论法,概率意义下的局部和整体Well-posedness,不变测度等。如果有时间我们还将涉及这些法近年的新发展。

 

 

 

Prerequisite:

 

 

 

实分析,调和分析,PDE的基础知识

 
 

 

 

Reference:

 

 

 

(for the first part)

 

 

 

Nonlinear Dispersive Equations: Local and Global Analysis, Terence Tao, CBMS Reg. Conf. Ser. Math. 106, Amer. Math. Soc., Providence, RI (2006)

 

 

 

(for the second part)

 

 

Nonlinear Schro ̈dinger equations, Jean Bourgain, In: Hyperbolic Equations and Frequency In- teractions (Park City, UT, 1995), IAS/Park City Math. Ser. 5, Amer. Math. Soc., 3–157 (1999)

 

 

Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I. Schrodinger equations, Jean Bourgain, Geom. Funct. Anal. 3, 209–262 (1993)

 

 

Periodic nonlinear Schro ̈dinger equation and invariant measures, Jean Bourgain, Comm. Math. Phys. 166, 1–26 (1994)

 

 

Invariant measures for the 2D-defocusing nonlinear Schro ̈dinger equation, Jean Bourgain, Comm. Math. Phys. 176, 421–445 (1996)

 

 

Almost sure well-posedness of the periodic cubic nonlinear Schrodinger equation below L2(T), James Colliander, Tadahiro Oh, Duke Math. J. 161, 367–414 (2012)

 

 

Probabilistic well-posedness for the cubic wave equation, Nicolas Burq, Nikolay Tzvetkov, J. Eur. Math. Soc. (JEMS) 16 (1), 1-30 (2014)