Dispersive estimates for full dispersion KP equations
| Autor: | Achenef Tesfahun, Jean-Claude Saut, Sigmund Selberg, Didier Pilod |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Physics
Applied Mathematics 010102 general mathematics Mathematical analysis Mathematics::Analysis of PDEs Condensed Matter Physics 01 natural sciences 010101 applied mathematics Computational Mathematics symbols.namesake Nonlinear Sciences::Exactly Solvable and Integrable Systems Mathematics - Analysis of PDEs Stationary phase Dispersion (optics) symbols FOS: Mathematics Initial value problem 0101 mathematics 35A01 35Q35 35Q53 42B20 Nonlinear Sciences::Pattern Formation and Solitons Mathematical Physics Bessel function Analysis of PDEs (math.AP) |
| Zdroj: | Journal of Mathematical Fluid Mechanics |
| Popis: | We prove several dispersive estimates for the linear part of the Full Dispersion Kadomtsev-Petviashvili introduced by David Lannes to overcome some shortcomings of the classical Kadomtsev-Petviashvili equations. The proof of these estimates combines the stationary phase method with sharp asymptotics on asymmetric Bessel functions, which may be of independent interest. As a consequence, we prove that the initial value problem associated to the Full Dispersion Kadomtsev-Petviashvili is locally well-posed in $H^s(\mathbb R^2)$, for $s>\frac74$, in the capillary-gravity setting. 29 pages, 3 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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