On the Cauchy problem for non-effectively hyperbolic operators,the Gevrey 5 well-posedness |
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Authors: | Enrico Bernardi Tatsuo Nishitani |
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Institution: | (1) Dipartimento di Matematica Per Le Scienze Economiche e Sociali, Università di Bologna, Viale Filopanti 5, 40126 Bologna, Italy;(2) Department of Mathematics, Osaka University, Machikaneyama 11, Toyonaka, 5600043 Osaka, Japan |
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Abstract: | In this paper, we prove that for non-effectively hyperbolic operators with smooth double characteristics exhibiting a Jordan
block of size 4 on the double manifold, the Cauchy problem is well-posed in the Gevrey 5 class, beyond the generic Gevrey
class 2 (see, e.g., 5]). Moreover, we show that this value is optimal, due to certain geometric constraints on the Hamiltonian
flow of the principal symbol. These results, together with results already proved, give a complete picture of the well-posedness
of the Cauchy problem around hyperbolic double characteristics. |
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Keywords: | |
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