Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5024704 | Nonlinear Analysis: Theory, Methods & Applications | 2017 | 19 Pages |
Abstract
We consider 1D equations with nonlocal velocity of the form wt+uwx+δuxw=âνÎγwwhere the nonlocal velocity u is given by (1) u=(1ââxx)âβw, β>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.
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Authors
Hantaek Bae, Dongho Chae, Hisashi Okamoto,