6 papers
Admissible solutions of the Euler equations
Alexey Cheskidov, Zirong Zeng, Deng Zhang
In this paper, we prove the existence of an extensive class of initial data--characterized by intermittency dimension and roughness--for which the d-dimensional Euler equations (d…
Global dissipative solutions of the 3D Naiver-Stokes and MHD equations
Alexey Cheskidov, Zirong Zeng, Deng Zhang
For any divergence free initial data in , we prove the existence of infinitely many dissipative solutions to both the 3D Navier-Stokes and MHD equations, whose energy pr…
Non-Leray-Hopf solutions to 3D stochastic hyper-viscous Navier-stokes equations: beyond the Lions exponents
Wenping Cao, Zirong Zeng, Deng Zhang
We consider the 3D stochastic Navier-Stokes equations (NSE) on torus where the viscosity exponent can be larger than the Lions exponent 5/4. For arbitrarily prescribed divergence-f…
Existence and non-uniqueness of probabilistically strong solutions to 3D stochastic magnetohydrodynamic equations
Wenping Cao, Yachun Li, Deng Zhang
We are concerned with the 3D stochastic magnetohydrodynamic (MHD) equations driven by additive noise on torus. For arbitrarily prescribed divergence-free initial data in ,…
Existence and non-uniqueness of weak solutions with continuous energy to the 3D deterministic and stochastic Navier-Stokes equations
Alexey Cheskidov, Zirong Zeng, Deng Zhang
The continuity of the kinetic energy is an important property of incompressible viscous fluid flows. We show that for any prescribed finite energy divergence-free initial data ther…
Non-uniqueness in law of Leray solutions to 3D forced stochastic Navier-Stokes equations
Elia Brué, Rui Jin, Yachun Li +1
This paper concerns the forced stochastic Navier-Stokes equation driven by additive noise in the three dimensional Euclidean space. By constructing an appropriate forcing term, we…