On the well-posedness of various one-dimensional model equations for fluid motion

被引：6

作者：

Bae, Hantaek ^{[1
]}

Chae, Dongho ^{[2
]}

Okamoto, Hisashi ^{[3
]}

机构：

[1] Ulsan Natl Inst Sci & Technol, Dept Math Sci, Ulsan, South Korea

[2] Chung Ang Univ, Dept Math, Seoul, South Korea

[3] Gakushuin Univ, Dept Math, Tokyo, Japan

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2017年 / 160卷

关键词：

1D model equations; Nonlocal velocity; Local well-posedness; Blow-up criterion; Global well-posedness; SHALLOW-WATER EQUATION; TRANSPORT-EQUATION; BLOW-UP; MAXIMUM PRINCIPLE; GLOBAL EXISTENCE; SINGULARITIES; EULER; BREAKING;

D O I：

10.1016/j.na.2017.05.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider 1D equations with nonlocal velocity of the form w(t) + uw(x) delta u(x)w = -v Lambda(gamma)w where the nonlocal velocity u is given by (1) u = (1-partial derivative(xx))-(beta)w, beta > 0 or (2) u = Hw H is the Hilbert transform). In this paper, we address several local well-posedness results with blow-up criteria for smooth initial data. We then establish the global well-posedness by using the blow-up criteria. (C) 2017 Elsevier Ltd. All rights reserved.

引用

页码：25 / 43

页数：19

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