• Corpus ID: 246015954

Local Martingale Solutions and Pathwise Uniqueness for the Three-dimensional Stochastic Inviscid Primitive Equations

@inproceedings{Hu2022LocalMS,
  title={Local Martingale Solutions and Pathwise Uniqueness for the Three-dimensional Stochastic Inviscid Primitive Equations},
  author={Ruimeng Hu and Quyuan Lin},
  year={2022}
}
We study the stochastic effect on the three-dimensional inviscid primitive equations (PEs, also called the hydrostatic Euler equations). Specifically, we consider a larger class of noises than multiplicative noises, and work in the analytic function space due to the ill-posedness in Sobolev spaces of PEs without horizontal viscosity. Under proper conditions, we prove the local existence of martingale solutions and pathwise uniqueness. By adding vertical viscosity, i.e., considering the… 
On the Effect of Fast Rotation and Vertical Viscosity on the Lifespan of the 3D Primitive Equations
We study the effect of the fast rotation and vertical viscosity on the lifespan of solutions to the three-dimensional primitive equations (also known as the hydrostatic Navier-Stokes equations) with

References

SHOWING 1-10 OF 53 REFERENCES
Stochastic Primitive Equations with Horizontal Viscosity and Diffusivity
We establish the existence and uniqueness of pathwise strong solutions to the stochastic 3D primitive equations with only horizontal viscosity and diffusivity driven by transport noise on a
Stable Singularity Formation for the Inviscid Primitive Equations
The primitive equations (PEs) model large scale dynamics of the oceans and the atmosphere. While it is by now well-known that the three-dimensional viscous PEs is globally well-posed in Sobolev
Strong pathwise solutions of the stochastic Navier-Stokes system
We consider the stochastic Navier-Stokes equations forced by a multiplicative white noise on a bounded domain in space dimensions two and three. We establish the local existence and uniqueness of
Pathwise Solutions of the 2-D Stochastic Primitive Equations
In this work we consider a stochastic version of the Primitive Equations (PEs) of the ocean and the atmosphere and establish the existence and uniqueness of pathwise, strong solutions. The analysis
Finite-Time Blowup for the Inviscid Primitive Equations of Oceanic and Atmospheric Dynamics
In an earlier work we have shown the global (for all initial data and all time) well-posedness of strong solutions to the three-dimensional viscous primitive equations of large scale oceanic and
Analyticity of Solutions for a Generalized Euler Equation
Abstract We consider the so-called lake and great lake equations, which are shallow water equations that describe the long-time motion of an inviscid, incompressible fluid contained in a shallow
...
...