Abstract
In this paper the subcritical Boussinesq system with fractional dissipation in T2 is considered. Our aim is to study the long-time behavior of solutions of Boussinesq system in its natural scale-invariant Sobolev space and prove the existence of a global attractor of optimal regularity. To this end we investigate the global well-posedness and global attractor for Boussinesq system in H2−α(T2)×H2−α(T2) via commutator estimates for nonlinear terms and a new energy estimate in Sobolev spaces to bootstrap the regularity, derived by means of nonlinear lower bounds on the fractional Laplacian. This estimate allows a sharp use of the subcritical nature of the L∞ bounds for this problem. Besides, we study the critical limit of the attractors and prove their stability and upper semicontinuity when α→1+.
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.