Probability Seminar——On ill- and well-posedness of dissipative martingale solutions to stochastic 3D Euler equations

2020-11-30 14:00-15:00 Room 1114, Sciences Building No. 1

Abstract: We are concerned with the question of well-posedness of stochastic three-dimensional incompressible Euler equations. In particular, we introduce a novel class of dissipative solutions and show that (i) existence; (ii) weak-strong uniqueness; (iii) non-uniqueness in law; (iv) existence of a strong Markov solution; (v) non-uniqueness of strong Markov solutions; all hold true within this class. Moreover, as a byproduct of (iii) we obtain existence and non-uniqueness of probabilistically strong and analytically weak solutions defined up to a stopping time and satisfying an energy inequality. This talk is based on joint work with Martina Hofmanova and Xiangchan Zhu.