Weak dispersion for the Dirac equation on asymptotically flat and warped product spaces

Federico Cacciafesta; Anne-Sophie  De Suzzoni

doi:10.3934/dcds.2019177

Article Contents

2019, Volume 39, Issue 8: 4359-4398. Doi: 10.3934/dcds.2019177

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Weak dispersion for the Dirac equation on asymptotically flat and warped product spaces

Federico Cacciafesta^1, , and
Anne-Sophie De Suzzoni^2,

1.
Dipartimento di Matematica, Università degli studi di Padova, Via Trieste, 63 35131 Padova PD, Italy
2.
École Polytechnique, CNRS Université Paris-Saclay, 91123 Palaiseau Cedex, France

^* Corresponding author: Federico Cacciafesta
^* Corresponding author: Federico Cacciafesta

Received: June 2018

Revised: February 2019

Published: May 2019

The second author is supported by ANR-18-CE40-0028 project ESSED

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Abstract

In this paper we prove local smoothing estimates for the Dirac equation on some non-flat manifolds; in particular, we will consider asymptotically flat and warped products metrics. The strategy of the proofs relies on the multiplier method.

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Mathematics Subject Classification: Primary: 35Q41, 35B40; Secondary: 35B06.

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References

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