Kappeler, T; Pöschel, J (2008). On the well-posedness of the periodic KdV equation in high regularity classes. In: Craig, W. Hamiltonian dynamical systems and applications. Dordrecht: Springer, 431-441.
We prove well-posedness results for the initial value problem of the periodic KdV equation in classes of high regularity solutions. More precisely, we consider the problem in weighted Sobolev spaces, which comprise classical Sobolev spaces, Gevrey spaces, and analytic spaces. We show that the initial value problem is well posed in all spaces with subexponential growth of Fourier coefficients, and ‘almost well posed’ in spaces with exponential growth of Fourier coefficients.
We prove well-posedness results for the initial value problem of the periodic KdV equation in classes of high regularity solutions. More precisely, we consider the problem in weighted Sobolev spaces, which comprise classical Sobolev spaces, Gevrey spaces, and analytic spaces. We show that the initial value problem is well posed in all spaces with subexponential growth of Fourier coefficients, and ‘almost well posed’ in spaces with exponential growth of Fourier coefficients.
| Item Type: | Book Section, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Scopus Subject Areas: | Life Sciences > Biotechnology
Life Sciences > Biophysics Physical Sciences > General Physics and Astronomy Physical Sciences > Electrical and Electronic Engineering |
| Language: | English |
| Date: | 2008 |
| Deposited On: | 09 Nov 2009 00:46 |
| Last Modified: | 30 Jun 2022 07:31 |
| Publisher: | Springer |
| Series Name: | NATO Science for Peace and Security Series B: Physics and Biophysics |
| ISSN: | 1874-6500 |
| ISBN: | 978-1-4020-6962-8 (Print) 978-1-4020-6964-2 (Online) |
| Additional Information: | Proceedings of the NATO Advanced Study Institute on Hamiltonian Dynamical Systems and Applications, Montreal, Canada, 18-29 June 2007 |
| OA Status: | Green |
| Publisher DOI: | https://doi.org/10.1007/978-1-4020-6964-2_18 |
| Related URLs: | http://www.poschel.de/pbl/well-posed-mon-1.pdf http://www.poschel.de/pbl/well-posed-mon-2.pdf |
Kappeler, T