Abstract
For a hyperbolic second-order differential operator , we study the relations between the maximal Gevrey index for the strong Gevrey well-posedness and some algebraic and geometric properties of the principal symbol . If the Hamilton map of (the linearization of the Hamilton field along double characteristics) has nonzero real eigenvalues at every double characteristic (the so-called effectively hyperbolic case), then it is well known that the Cauchy problem for is well posed in any Gevrey class for any lower-order term. In this paper we prove that if is noneffectively hyperbolic and, moreover, such that on a double characteristic manifold of codimension , assuming that there is no null bicharacteristic landing tangentially, then the Cauchy problem for is well posed in the Gevrey class for any lower-order term (strong Gevrey well-posedness with threshold ), extending in particular via energy estimates a previous result of Hörmander in a model case.
Citation
Enrico Bernardi. Tatsuo Nishitani. "On the Cauchy problem for noneffectively hyperbolic operators: The Gevrey 4 well-posedness." Kyoto J. Math. 51 (4) 767 - 810, Winter 2011. https://doi.org/10.1215/21562261-1424857
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