
2月演講

PDE Seminar, 成功大學數學系 吳恭儉教授
Wednesday, February 13, 11:10—15:00 數學系3樓會議室
Title: Milne Problem Abstract: Stationary halfspace solutions of the linearized Boltzmann equation with hard potential are studied by energy estimate methods. I will present existence, uniqueness and asymptotic behavior of this problem.

Colloquium, 京都大學數學系 Prof. Yoshio Tsutsumi
Thursday, February 21, 15:10—16:00 數學系3174
Title: IllPosedness of the Third Order NLS Equation with Raman Scattering Term Abstract: We consider the illposedness of the Cauchy problem for the third order NLS equation with Raman scattering term on the one dimensional torus. It has been universally used among physicists as a mathematical model for the photonic crystal fiber oscillator (see, e.g., [1]). I show the nonexistence of solutions in the Sobolev space and the norm inflation of the datasolution map at the origin under slightly different conditions, respectively. Physicists sometimes propose models which have strong instability from a mathematical point of view. Equation (1) is such a kind of example and it is not very clear what role the mathematical illposedness plays in physics. I also talk about the local unique existence of solutions in the analytic function space. This talk is based on the joint work [2] with Nobu Kishimoto, RIMS, Kyoto University. References [1] G. Agrawal, Nonlinear Fiber Optics, 4th edition, Elsevier / Academic Press, Burlington, 2007. [2] N. Kishimoto and Y. Tsutsumi, Illposedness of the third order NLS equation with Raman scattering term, preprint, arXiv: 1706.09111v1 [math.AP]

Colloquium, 京都大學數學系 Prof. Yoshio Tsutsumi
Thursday, February 21, 16:10—17:00 數學系3174
Title: QuasiInvariant Gaussian Measures for NLS with Third Order Dispersion Abstract: Invariant measures for nonlinear evolution equations have been attracted the attention of many researchers. Especially, the Gibbs measure for the Hamiltonian system is natural and important from both mathematical and physical points of view. However, the support of the Gibbs measure is determined by the Hamiltonian of the system in question and it is often a weak function space. Therefore, the Gibbs measure does not capture smooth solutions such as finite energy solutions. Recently, Tzvetkov showed the quasiinvariant property of Gaussian measures with support including smooth solutions for some nonlinear dispersive equations instead of the invariant property. It is very interesting, because the quasiinvariance might be able to replace the role of invariance. In this talk, I will talk about the quasiinvariance of certain Gaussian measures for NLS with third order dispersion. This is a joint work with Nikolay Tzvetkov (University of CergyPontoise) and Tadahiro Oh (University of Edinburgh).





