Low regularity well-posedness for two-dimensional deep gravity water waves with constant vorticity

被引：0

作者：

Wan, Lizhe ^{[1
]}

机构：

[1] Univ Wisconsin Madison, Dept Math, Madison, WI 53706 USA

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2025年 / 50卷 / 1-2期

关键词：

Balanced energy estimate; constant vorticity; holomorphic coordinates; FREE-SURFACE; MOTION; FLUID;

D O I：

10.1080/03605302.2024.2436407

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the two-dimensional gravity water waves with nonzero constant vorticity in infinite depth. We show that for s >= 34, the water waves system is locally well-posed in Hs, which is the nonzero constant vorticity counterpart of the breakthrough work of Ai-Ifrim-Tataru. It is also a 14 improvement in Sobolev regularity compared to the previous result of Ifrim-Tataru.

引用

页码：53 / 117

页数：65

共 50 条

[21] Low regularity well-posedness for nonlinear wave equations
Dept. of Mathematics, Southwest Jiaotong University, Chengdu 610031, China
不详
Xinan Jiaotong Daxue Xuebao, 2006, 1 (127-130):
[22] Well-Posedness and Shallow-Water Stability for a New Hamiltonian Formulation of the Water Waves Equations with Vorticity
Castro, Angel
Lannes, David
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2015, 64 (04) : 1169 - 1270
[23] WELL-POSEDNESS OF A MODEL FOR WATER WAVES WITH VISCOSITY
Ambrose, David M.
Bona, Jerry L.
Nicholls, David P.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2012, 17 (04): : 1113 - 1137
[24] Well-posedness of the water-waves equations
Lannes, D
JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2005, 18 (03) : 605 - 654
[25] WELL-POSEDNESS OF EVOLUTIONARY NAVIER-STOKES EQUATIONS WITH FORCES OF LOW REGULARITY ON TWO-DIMENSIONAL DOMAINS (vol 27, 61, 2021)
CASAS, E. D. U. A. R. D. O.
KUNISCH, K. A. R. L.
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2022, 28
[26] On the global well-posedness for the two-dimensional Boussinesq equations with horizontal dissipation
Guo, Meiqi
Zhang, Qian
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2019, 42 (01) : 322 - 345
[27] WELL-POSEDNESS FOR THE TWO-DIMENSIONAL MODIFIED ZAKHAROV-KUZNETSOV EQUATION
Linares, Felipe
Pastor, Ademir
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2009, 41 (04) : 1323 - 1339
[28] Nonlinear two-dimensional water waves with arbitrary vorticity
Ionescu-Kruse, Delia
Ivanov, Rossen
JOURNAL OF DIFFERENTIAL EQUATIONS, 2023, 368 : 317 - 349
[29] Global well-posedness of the two-dimensional Benjamin equation in the energy space
Chen, Wengu
Wei, Suqing
Li, Junfeng
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2019, 45 : 755 - 788
[30] Well-posedness of the two-dimensional nonlinear Schrodinger equation with concentrated nonlinearity
Carlone, Raffaele
Correggi, Michele
Tentarelli, Lorenzo
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2019, 36 (01): : 257 - 294

← 1 2 3 4 5 →