On Maslov Conjecture about Square Root Type Singular Solutions of the Shallow Water Equations

TL;DR

This paper proves Maslov's conjecture that the square root structure of quadratic forms uniquely characterizes weakly singular solutions of the shallow water equations, crucial for understanding vortex dynamics and typhoon paths.

Contribution

It establishes the uniqueness of the square root structure in weakly singular solutions of the shallow water equations, confirming a key conjecture by Maslov.

Findings

Confirmed the uniqueness of the square root structure in solutions

Linked the structure to vortex dynamics and typhoon modeling

Provided a mathematical foundation for singular solution analysis

Abstract

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.