Abstract
We study the nonlinear almost compressible 2D Oberbeck-Boussinesq system, characterized by an extra buoyancy term where the density depends on the pressure, and a corresponding dimensionless parameter β, proportional to the (positive) compressibility factor β0. The local in time existence of the perturbation to the conductive solution is proved for any “size” of the initial data. However, unlike the classical problem where β0 = 0, a smallness condition on the initial data is needed for global in time existence, along with smallness of the Rayleigh number. Removing this condition appears quite challenging, and we leave it as an open question.We study the nonlinear almost compressible 2D Oberbeck-Boussinesq system, characterized by an extra buoyancy term where the density depends on the pressure, and a corresponding dimensionless parameter β, proportional to the (positive) compressibility factor β0. The local in time existence of the perturbation to the conductive solution is proved for any “size” of the initial data. However, unlike the classical problem where β0 = 0, a smallness condition on the initial data is needed for global in time existence, along with smallness of the Rayleigh number. Removing this condition appears quite challenging, and we leave it as an open question.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.