Escher, Joachim and Knopf, Patrik and Lienstromberg, Christina and Matioc, Bogdan-Vasile (2020) Stratified periodic water waves with singular density gradients. ANNALI DI MATEMATICA PURA ED APPLICATA, 199 (5). pp. 1923-1959. ISSN 0373-3114, 1618-1891
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We consider Euler's equations for free surface waves traveling on a body of density stratified water in the scenario when gravity and surface tension act as restoring forces. The flow is continuously stratified, and the water layer is bounded from below by an impermeable horizontal bed. For this problem we establish three equivalent classical formulations in a suitable setting of strong solutions which may describe nevertheless waves with singular density gradients. Based upon this equivalence we then construct two-dimensional symmetric periodic traveling waves that are monotone between each crest and trough. Our analysis uses, to a large extent, the availability of a weak formulation of the water wave problem, the regularity properties of the corresponding weak solutions, and methods from nonlinear functional analysis.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | CAPILLARY-GRAVITY WAVES; GLOBAL BIFURCATION; EQUATORIAL FLOWS; FREE-SURFACE; EDGE WAVES; REGULARITY; ANALYTICITY; EXISTENCE; Euler equations; Traveling waves; Stratified fluid; Singular density gradient |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 30 Mar 2021 12:26 |
| Last Modified: | 30 Mar 2021 12:26 |
| URI: | https://pred.uni-regensburg.de/id/eprint/45133 |
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