On the V-states for the generalized quasi-geostrophic equations. (English) Zbl 1319.35188
In this article the authors study a generalized surface quasigeostrophic system introduced by D. Córdoba et al. [Proc. Natl. Acad. Sci. USA 102, No. 17, 5949–5952 (2005; Zbl 1135.76315)] as a model of atmospheric-oceanic flow, interpolating through a parameter \(0\leq\alpha\leq 1\) between the inviscid Euler system (\(\alpha=0\)) and the surface quasigeostrophic system (\(\alpha=1\)). They concentrate on particular vortex solutions called V-states, introduced by G. S. Deem and N. J. Zabusky, [“Vortex waves: stationary “V-states”, interactions, recurrence, and breaking”, Phys. Rev. Lett. 40(13), 859–862 (1978)] as rotating patches: simply connected, rigidly rotating domains.
They extend previous works on the Euler system for \(\alpha=0\) to the \(\alpha>0\) case, using the bifurcation machinery of Crandall-Rabinowitz and singular integrals arguments, allowing them to prove existence of an infinite family of non stationary global solutions.
They extend previous works on the Euler system for \(\alpha=0\) to the \(\alpha>0\) case, using the bifurcation machinery of Crandall-Rabinowitz and singular integrals arguments, allowing them to prove existence of an infinite family of non stationary global solutions.
Reviewer: Bernard Ducomet (Bruyères le Châtel)
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 86A05 | Hydrology, hydrography, oceanography |
Citations:
Zbl 1135.76315References:
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