本文主要研究内容
作者（2019）在《MULTIPLE VORTICES FOR THE SHALLOW WATER EQUATION IN TWO DIMENSIONS》一文中研究指出：In this paper, we construct stationary classical solutions of the shallow water equation with vanishing Froude number F r in the so-called lake model.To this end we need to study solutions to the following semilinear elliptic problem ■ for small ε > 0, where p > 1, div(?q/b)= 0 and ? ? R~2 is a smooth bounded domain.We show that if q2/b has m strictly local minimum(maximum) points ■, i =1,···, m, then there is a stationary classical solution approximating stationary m points vortex solution of shallow water equations with vorticity ■.Moreover, strictly local minimum points of q2/b on the boundary can also give vortex solutions for the shallow water equation.
Abstract
In this paper, we construct stationary classical solutions of the shallow water equation with vanishing Froude number F r in the so-called lake model.To this end we need to study solutions to the following semilinear elliptic problem ■ for small ε > 0, where p > 1, div(?q/b)= 0 and ? ? R~2 is a smooth bounded domain.We show that if q2/b has m strictly local minimum(maximum) points ■, i =1,···, m, then there is a stationary classical solution approximating stationary m points vortex solution of shallow water equations with vorticity ■.Moreover, strictly local minimum points of q2/b on the boundary can also give vortex solutions for the shallow water equation.
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