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

Bae, Hantaek; Chae, Dongho; Okamoto, Hisashi

doi:10.1016/j.na.2017.05.002

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

Bae, Hantaek;
Chae, Dongho;
Okamoto, Hisashi

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6

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6

초록

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.

키워드

1D model equations; Nonlocal velocity; Local well-posedness; Blow-up criterion; Global well-posedness; 3-DIMENSIONAL VORTICITY EQUATION; QUASI-GEOSTROPHIC EQUATIONS; NAVIER-STOKES EQUATIONS; SHALLOW-WATER EQUATION; NONLOCAL VELOCITY; TRANSPORT-EQUATION; BLOW-UP; MAXIMUM PRINCIPLE; GLOBAL EXISTENCE; EULER EQUATIONS

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

저자: Bae, Hantaek; Chae, Dongho; Okamoto, Hisashi

DOI: 10.1016/j.na.2017.05.002

발행일: 2017-09

유형: Article

저널명: Nonlinear Analysis, Theory, Methods and Applications

권: 160

페이지: 25 ~ 43