On Ill- and Well-Posedness of Dissipative Martingale Solutions to Stochastic 3D Euler Equations(Xiangchan Zhu)----Academy of Mathematics and Systems Science

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

Publication:

- COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, (2021)

Authors:

- Martina Hofmanova (Fakultat f ¨ ur Mathematik, Universit ¨ at Bielefeld)

- Rongchan Zhu (Department of Mathematics, Beijing Institute of Technology)

- Xiangchan Zhu (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)