About this Event
3620 South Vermont Avenue, Los Angeles, CA 90089
Fred Weissler, University Sorbonne Paris Nord
Abstract: After rapidly reviewing the history of the Korteweg-deVries equation, I will discuss the issues of local and global well-posedness for complex-valued solutions on the circle. In particular, a large class of local-in time solutions develop a singularity in finite time. Hence global well-posedness can fail.
In addition, local well-posedness can fail for two reasons. There exist initial values with no reasonable local-in time solution. Also, if complex-valued solutions are considered, continuous dependence fails at the zero solution. These results are of course completely at variance with the well-known results for real-valued solutions.