Local Well-Posedness of an Approximate Equation for SQG Fronts

Local Well-Posedness of an Approximate Equation for SQG Fronts

We prove local well-posedness in the Sobolev spaces H ˙ s ( T ) , with s > 7 / 2 , of an initial value problem for a nonlocal, cubically nonlinear, dispersive equation that provides an approximate description of the evolution of surface quasi-geostrophic fronts with small slopes.

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Veröffentlicht in:Journal of mathematical fluid mechanics 2018-12, Vol.20 (4), p.1967-1984
Hauptverfasser: Hunter, John K., Shu, Jingyang, Zhang, Qingtian
Format: Artikel
Sprache:eng
Schlagworte:
Boundary value problems
Classical and Continuum Physics
Fluid mechanics
Fluid- and Aerodynamics
Mathematical Methods in Physics
Physics
Physics and Astronomy
Sobolev space
Theoretical mathematics
Well posed problems
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Zusammenfassung:We prove local well-posedness in the Sobolev spaces H ˙ s ( T ) , with s > 7 / 2 , of an initial value problem for a nonlocal, cubically nonlinear, dispersive equation that provides an approximate description of the evolution of surface quasi-geostrophic fronts with small slopes.
ISSN:1422-6928
1422-6952
DOI:10.1007/s00021-018-0396-z