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Proof of Maslov’s conjecture about the structure of weak point singular solutions of the shallow water equations. (English) Zbl 1082.35513
Summary: We prove Maslov’s conjecture that the structure of the type of square root of a quadratic form is the unique structure of weakly singular solutions (with a point singularity) of the shallow water equations with the properties of asymptotic self-similarity and stability. This fact plays a key role in the study of the dynamics of vortical singularities and their applications to the description of typhoon trajectories.
35L60 First-order nonlinear hyperbolic equations
35L67 Shocks and singularities for hyperbolic equations
35Q35 PDEs in connection with fluid mechanics
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction