On ill- and well-posedness of dissipative martingale solutions to stochastic 3D Euler equations
arXiv:2009.09552
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.
References in corpus (7)
- On admissibility criteria for weak solutions of the Euler equations
- Solution properties of a 3D stochastic Euler fluid equation
- Existence and uniqueness for stochastic 2D Euler flows with bounded vorticity
- On solvability and ill-posedness of the compressible Euler system subject to stochastic forces
- Global well-posedness of the 3D Navier--Stokes equations perturbed by a deterministic vector field
- Remarks on the non-uniqueness in law of the Navier-Stokes equations up to the J.-L. Lions' exponent
- Non-uniqueness in law of stochastic 3D Navier--Stokes equations