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In this paper, we construct stationary classical solutions of the shallowwater equation with vanishing Froude number $Fr$ in the so-called lake model.  To this end we need to study solutions to the following semilinear ellipticproblem \[{cases} -\varepsilon^2\text{div}(\frac{\nablau}{b})=b(u-q\log\frac{1}{\varepsilon})_+^{p},& \text{in}\; \Omega, u=0,&\text{on}\;\partial \Omega, {cases} \] for small $\varepsilon>0$, where $p>1$,$\text{div}(\frac{\nabla q}{b})=0$ and $\Omega\subset\mathbb{R}^2$ is a smoothbounded domain,.  We showed that if $\frac{q^2}{b}$ has $m$ strictly local minimum(maximum)points $\bar z_i,\,i=1,...,m$, then there is a stationary classical solutionapproximating stationary $m$ points vortex solution of shallow water equationswith vorticity $\sum_{i=1}^m\frac{2\pi q(\bar z_i)}{b(\bar z_i)}$. Moreover,strictly local minimum points of $\frac{q^2}{b}$ on the boundary can also givevortex solutions for the shallow water equation. As a further study weconstruct vortex pair solutions as well.  Existence and asymptotic behavior of single point non-vanishing vortexsolutions were studied by S. De Valeriola and J. Van Schaftingen.

Multiple Vortices for the Shallow Water Equation