Non-uniqueness in law for Boussinesq system forced by random noise
Kazuo Yamazaki
TL;DR
This paper proves non-uniqueness in law for the three-dimensional Boussinesq system with random noise, extending recent results from Navier-Stokes equations to include temperature scalar fields with full Laplacian diffusion.
Contribution
It establishes non-uniqueness in law for the Boussinesq system with stochastic forcing, a novel extension of prior work on Navier-Stokes equations.
Findings
Non-uniqueness in law proven for Boussinesq system with noise
Temperature scalar field can be initially smooth
Results extend stochastic non-uniqueness to coupled fluid-temperature systems
Abstract
Non-uniqueness in law for three-dimensional Navier-Stokes equations forced by random noise was established recently in Hofmanov et al. (2019, arXiv:1912.11841 [math.PR]). The purpose of this work is to prove non-uniqueness in law for the Boussinesq system forced by random noise. Diffusion within the equation of its temperature scalar field has a full Laplacian and the temperature scalar field can be initially smooth.
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