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- Bae, Hantaek
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ON THE LOCAL AND GLOBAL EXISTENCE OF SOLUTIONS TO 1D TRANSPORT EQUATIONS WITH NONLOCAL VELOCITY
- Author(s)
- Bae, Hantaek, Granero-Belinchon, Rafael, Lazar, Omar
- Issued Date
- 2019-09
- Citation
- NETWORKS AND HETEROGENEOUS MEDIA, v.14, no.3, pp.471 - 487
- Abstract
- We consider the 1D transport equation with nonlocal velocity field: theta(t) + u theta(x) + nu Lambda(gamma)theta = 0, u = N(theta), where N is a nonlocal operator and Lambda(gamma) is a Fourier multiplier defined by (Lambda gamma f) over cap(xi) =vertical bar xi vertical bar(gamma)(f) over cap(xi). In this paper, we show the existence of solutions of this model locally and globally in time for various types of nonlocal operators.
- Publisher
- AMER INST MATHEMATICAL SCIENCES-AIMS
- ISSN
- 1556-1801
- Keyword (Author)
- Fluid equations, 1D models, global weak solution
- Keyword
- ONE-DIMENSIONAL MODEL, WELL-POSEDNESS, BLOW-UP, SINGULARITIES
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