Convergence of stochastic 2D inviscid Boussinesq equations with transport noise to a deterministic viscous system

Perturbation of Stochastic Boussinesq Equations with Multiplicative White Noise

The Boussinesq equation is a mathematics model of thermohydraulics, which consists of equations of fluid and temperature in the Boussinesq approximation.The deterministic case has been studied systematically by many authors (e.g., see [1– 3]). However, in many practical circumstances, small irregularity has to be taken into account.Thus, it is necessary to add to the equation a random force, wh...

Inviscid Limit of Stochastic Damped 2d Navier-stokes Equations

We consider the inviscid limit of the stochastic damped 2D NavierStokes equations. We prove that, when the viscosity vanishes, the stationary solution of the stochastic damped Navier-Stokes equations converges to a stationary solution of the stochastic damped Euler equation and that the rate of dissipation of enstrophy converges to zero. In particular, this limit obeys an enstrophy balance. The...

Blowup in stagnation-point form solutions of the inviscid 2d Boussinesq equations

The 2d Boussinesq equations model large scale atmospheric and oceanic flows. Whether its solutions develop a singularity in finite-time remains a classical open problem in mathematical fluid dynamics. In this work, blowup from smooth nontrivial initial velocities in stagnation-point form solutions of this system is established. On an infinite strip = {(x, y) ∈ [0, 1] × R+}, we consider velociti...

The 2D Incompressible Boussinesq Equations

Yudovich type solution for the 2D inviscid Boussinesq system with critical and supercritical dissipation

In this paper we consider the Yudovich type solution of the 2D inviscid Boussinesq system with critical and supercritical dissipation. For the critical case, we show that the system admits a global and unique Yudovich type solution; for the supercritical case, we prove the local and unique existence of Yudovich type solution, and the global result under a smallness condition of θ0. We also give...