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- Bae, Hantaek
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On the well-posedness of various one-dimensional model equations for fluid motion
- Author(s)
- Bae, Hantaek, Chae, Dongho, Okamoto, Hisashi
- Issued Date
- 2017-09
- Citation
- NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, v.160, pp.25 - 43
- Abstract
-
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.
- Publisher
- PERGAMON-ELSEVIER SCIENCE LTD
- ISSN
- 0362-546X
- Keyword (Author)
- 1D model equations, Blow-up criterion, Global well-posedness, Local well-posedness, Nonlocal velocity
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