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Analytic sharp fronts for the surface quasi-geostrophic equation. (English) Zbl 1228.35010
This work is concerned with the evolution of sharp fronts for the quasi-geostrophic surface waves. The nonlinear integro-differential equation governing the evolution wave fronts in such flows was already obtained. The authors consider a simplified version of this equation and study the existence of analytical solutions through extensive calculations. By carefully investigating the evolution of the second space derivative of the unknown function the authors prove that the new system fits well into the abstract version of the celebrated Cauchy-Kovalevskaya theorem.
MSC:
35A10Cauchy-Kowalewski theorems
76B15Water waves, gravity waves; dispersion and scattering, nonlinear interaction
35R11Fractional partial differential equations
References:
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