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EnglishIn this paper we study the well-posedness of the Cauchy problem for first order hyperbolic systems with constant multiplicities and with low regularity coefficients depending just on the time variable. We consider Zygmund and log-Zygmund type assumptions, and we prove well-posedness in H^\infty respectively without loss and with finite loss of derivatives. The key to obtain the results is the construction of a suitable symmetrizer for our system, which allows us to recover energy estimates (with or without loss) for the hyperbolic operator under consideration. This can be achievied, in contrast with the classical case of systems with smooth (say Lipschitz) coefficients, by adding one step in the diagonalization process, and building the symmetrizer up to the second order.
| Titolo: | The well-posedness issue in Sobolev spaces for hyperbolic systems with Zygmund-type coefficients |
| Autori: | |
| Data di pubblicazione: | 2015 |
| Rivista: | |
| Abstract: | In this paper we study the well-posedness of the Cauchy problem for first order hyperbolic systems with constant multiplicities and with low regularity coefficients depending just on the time variable. We consider Zygmund and log-Zygmund type assumptions, and we prove well-posedness in H^\infty respectively without loss and with finite loss of derivatives. The key to obtain the results is the construction of a suitable symmetrizer for our system, which allows us to recover energy estimates (with or without loss) for the hyperbolic operator under consideration. This can be achievied, in contrast with the classical case of systems with smooth (say Lipschitz) coefficients, by adding one step in the diagonalization process, and building the symmetrizer up to the second order. |
| Handle: | http://hdl.handle.net/11368/2851862 |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1080/03605302.2015.1082107 |
| URL: | http://www.tandfonline.com/loi/lpde20 |
| Appare nelle tipologie: | 1.1 Articolo in Rivista |
File in questo prodotto:
| File | Descrizione | Tipologia | Licenza | |
|---|---|---|---|---|
| 03605302%2E2015%2E1082107.pdf | Articolo | Documento in Versione Editoriale | Digital Rights Management non definito | Administrator Richiedi una copia |
| C-DS-F-M_systems.06.02.14.pdf | articolo | Bozza finale post-referaggio (post-print) | Digital Rights Management non definito | Open Access Visualizza/Apri |
http://hdl.handle.net/11368/2851862
