Abstract
This paper is concerned with the study of a non-local Burgers equation for positive bounded periodic initial data. The equation reads u_t − u|∇|u + |∇|(u^2) = 0. We construct global classical solutions starting from smooth positive data, and global weak solutions starting from data in L ∞. We show that any weak solution is instantaneously regularized into C ∞. We also describe the long-time behavior of all solutions. Our methods follow several recent advances in the regularity theory of parabolic integro-differential equations.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Annales de la Faculté des sciences de Toulouse : Mathématiques
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.
