On the spectrum and bases of eigenfunctions of a~problem connected with oscillations of a~rotating fluid

S. A. Gabov

Sbornik. Mathematics, Tome 44 (1983) no. 2, pp. 219-226

Résumé

The author considers the eigenvalue problem \begin{gather*} \Delta u-\mu^2\,\frac{\lambda^2-k^2}{\lambda^2-\beta^2}\,u=0,\qquad x\in D\subset\mathbf R^2, \\ \frac{\partial u}{\partial n}+i\,\frac k\lambda\,\frac{\partial u}{\partial \tau}=0, \qquad x\in\partial D, \end{gather*} which arises in studying the problem of normal oscillations of a rotating exponentially stratified liquid in a cylindrical container. It is shown that the spectrum is real and localized in the neighborhood of two limit points $\lambda=\pm\beta$, and the system of eigenvalues forms a two-fold Riesz basis in $L_2(D)$. Bibliography: 9 titles.