Frederic Weissler : Blow up and local ill-posedness for the the complex, periodic Korteweg-DeVries equation

Posted by Christof Sparber , part of the Analysis and Applied Mathematics Seminar.

At

Dec. 7, 2023, 4 p.m.

In

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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.