Non-uniqueness in law for Boussinesq system forced by random noise

Abstract

Non-uniqueness in law for three-dimensional Navier-Stokes equations forced by random noise was established recently in Hofmanov$\acute{\mathrm{a}}$ 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.

The range of the exponent of a fractional Laplacian in the 3D case has been expanded. Some other structural changes have been made. This preprint has not undergone peer review or any post-submission improvements or corrections

References in corpus (4)

• Large deviations for the Boussinesq Equations under Random Influences
• Remarks on the non-uniqueness in law of the Navier-Stokes equations up to the J.-L. Lions' exponent
• On ill- and well-posedness of dissipative martingale solutions to stochastic 3D Euler equations
• Non-uniqueness in law for two-dimensional Navier-Stokes equations with diffusion weaker than a full Laplacian

Cited by in corpus (2)

• On Onsager's type conjecture for the inviscid Boussinesq equations
• Global-in-time probabilistically strong and Markov solutions to stochastic 3D Navier--Stokes equations: existence and non-uniqueness