On the well-posedness of stochastic boussinesq equations with transport noise

Abstract

Open access at https://arxiv.org/pdf/1807.09493.pdf.The Boussinesq equations play a fundamental role in meteorology. Among other aspects, they aim to model the process of frontogenesis and describe large-scale atmospheric and oceanic flows. In this work, we establish the existence and uniqueness of maximal strong solutions of the stochastic Boussinesq equations with transport noise in Sobolev spaces and construct a blow-up criterion. For this, in particular, we derive some general estimates, which turn out to be crucial for showing the well-posedness of a broader range of stochastic partial differential equations.The first author has been partially supported by the Grant MTM2017-83496-P from the Spanish Ministry of Economy and Competitiveness and through the Severo Ochoa Programme for Centres of Excellence in R&D (SEV-2015-0554). The second author has been supported by the Mathematics of Planet Earth Centre of Doctoral Training (MPE CDT) and Grantham Research Institute on Climate Change and the Environment, London School of Economics and Political Science