On the well-posedness of stochastic Boussinesq equations with cylindrical multiplicative noise

Abstract

The Boussinesq equations are fundamental in meteorology. Among other aspects, they aim to model the process of front formation. We use the approach presented in [Hol15] to introduce stochasticity into the incompressible Boussinesq equations. This is, we introduce cylindrical transport noise in a way that the geometric properties in the Euler-Poincaré formulation are preserved. One of our main results establishes the local well-posedness of regular solutions for these new stochastic Boussinesq equations. We also construct a blow-up criterion and derive some general estimates, which are crucial for showing well-posedness of a wide range of similar SPDEs.

arXiv comment42 pages

References in corpus (4)

• Variational Principles for Stochastic Fluid Dynamics
• Solution properties of a 3D stochastic Euler fluid equation
• Large deviations for the Boussinesq Equations under Random Influences
• Stability, well-posedness and blow-up criterion for the Incompressible Slice Model

Cited by in corpus (6)

• Modelling the climate and weather of a 2D Lagrangian-averaged Euler-Boussinesq equation with transport noise
• Convergence of stochastic 2D inviscid Boussinesq equations with transport noise to a deterministic viscous system
• Deterministic and Stochastic Euler-Boussinesq Convection
• Stochastic transport equations with unbounded divergence
• Existence and Uniqueness of Maximal Solutions to a 3D Navier-Stokes Equation with Stochastic Lie Transport
• A local-in-time theory for singular SDEs with applications to fluid models with transport noise