Journal article
Small strong solutions for time-dependent mean field games with local coupling
Comptes rendus. Mathématique, v 354(6), pp 589-594
01 Jun 2016
Abstract
For mean field games with local coupling, existence results are typically for weak solutions rather than strong solutions. We identify conditions on the Hamiltonian and the coupling, which allow us to prove the existence of small, locally unique, strong solutions over any finite time interval in the case of local coupling; these conditions place us in the case of superquadratic Hamiltonians. For the regularity of solutions, we find that at each time in the interior of the time interval, the Fourier coefficients of the solutions decay exponentially. The method of proof is inspired by the work of Duchon and Robert on vortex sheets in incompressible fluids. (C) 2016 Academie des sciences. Published by Elsevier Masson SAS. Allrightsreserved.
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Details
- Title
- Small strong solutions for time-dependent mean field games with local coupling
- Creators
- David M. Ambrose - Drexel University
- Publication Details
- Comptes rendus. Mathématique, v 354(6), pp 589-594
- Publisher
- Elsevier
- Number of pages
- 6
- Grant note
- DMS-1016267; DMS-1515849 / National Science Foundation; National Science Foundation (NSF) 1515849 / Direct For Mathematical & Physical Scien; National Science Foundation (NSF); NSF - Directorate for Mathematical & Physical Sciences (MPS)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000377533000009
- Scopus ID
- 2-s2.0-84964751489
- Other Identifier
- 991019168396304721
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- Web of Science research areas
- Mathematics