Long wave asymptotics for the Euler–Korteweg system
| Autor: | David Chiron, Sylvie Benzoni-Gavage |
|---|---|
| Přispěvatelé: | Laboratoire Jean Alexandre Dieudonné (JAD), Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Modélisation mathématique, calcul scientifique (MMCS), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), ANR-13-BS01-0009,BoND,Frontières, numérique, dispersion.(2013), ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010) |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
General Mathematics
Mathematics::Analysis of PDEs Key-words: Euler–Korteweg system Kadomtsev–Petviashvili equation 01 natural sciences capillary fluids symbols.namesake Inviscid flow [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] 0101 mathematics Korteweg de Vries equation Korteweg–de Vries equation Nonlinear Schrödinger equation Nonlinear Sciences::Pattern Formation and Solitons Mathematics Kadomtsev-Petviashvili equation 010102 general mathematics Mathematical analysis Acoustic wave 010101 applied mathematics Nonlinear system Amplitude Nonlinear Sciences::Exactly Solvable and Integrable Systems weakly transverse Boussinesq system Euler's formula symbols |
| Zdroj: | Revista Matemática Iberoamericana Revista Matemática Iberoamericana, European Mathematical Society, 2018, 34 (1), pp.245-304. ⟨10.4171/RMI/985⟩ |
| ISSN: | 0213-2230 |
| DOI: | 10.4171/RMI/985⟩ |
| Popis: | International audience; The Euler–Korteweg system (EK) is a fairly general nonlinear waves model in mathematical physics that includes in particular the fluid formulation of the NonLinear Schrödinger equation (NLS). Several asymptotic regimes can be considered, regarding the length and the amplitude of waves. The first one is the free wave regime, which yields long acoustic waves of small amplitude. The other regimes describe a single wave or two counter propagating waves emerging from the wave regime. It is shown that in one space dimension those waves are governed either by inviscid Burgers or by Korteweg-de Vries equations, depending on the spatio-temporal and amplitude scalings. In higher dimensions, those waves are found to solve Kadomtsev-Petviashvili equations. Error bounds are provided in all cases. These results extend earlier work on defocussing (NLS) (and more specifically the Gross–Pitaevskii equation), and sheds light on the qualitative behavior of solutions to (EK), which is a highly nonlinear system of PDEs that is much less understood in general than (NLS). |
| Databáze: | OpenAIRE |
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