Analysis and Applied Mathematics Seminar
Frederic Weissler
Université Sorbonne
Blow up and local ill-posedness for the the complex, periodic Korteweg-DeVries equation
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.
Thursday December 7, 2023 at 4:00 PM in 636 SEO