6 papers
FrontierCS: Evolving Challenges for Evolving Intelligence
Qiuyang Mang, Wenhao Chai, Zhifei Li +48
We introduce FrontierCS, a benchmark of 156 open-ended problems across diverse areas of computer science, designed and reviewed by experts, including CS PhDs and top-tier competiti…
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…
Sharp non-uniqueness for the 3D hyperdissipative Navier-Stokes equations: above the Lions exponent
Yachun Li, Peng Qu, Zirong Zeng +1
We study the 3D hyperdissipative Navier-Stokes equations on the torus, where the viscosity exponent can be larger than the Lions exponent . It is well-known that, due to L…
A Boundary Value Problem for a Class of Anisotropic Stochastic Degenerate Parabolic-Hyperbolic Equations
Hermano Frid, Yachun Li, Daniel Marroquin +2
We establish the well-posedness of an initial-boundary value problem of mixed type for a stochastic nonlinear parabolic-hyperbolic equation on a space domain $\cO=\cO'\X\cO''$ wher…
The Strong Trace Property and the Neumann Problem for Stochastic Conservation Laws
Hermano Frid, Yachun Li, Daniel Marroquin +2
We establish the well-posedness of the Neumann problem for stochastic conservation laws with multiplicative noise. As a major step for establishing the uniqueness of the kinetic so…