A generalized biharmonic equation and its applications to hydrodynamic stability

A generalized biharmonic equation and its applications to hydrodynamic instability

“…Next, we apply corollary 3 of theorem 2 to the system of equations and boundary conditions given in the following sections corresponding to the thermohaline instability problems of the Veronis and Stern types for a viscoelastic liquid and derive thereupon in a unified manner the results already established by the usual Pellew and Southwell technique with slight modifications (Gupta et al 1985).…”

“…Several such results exist concerning problems in hydrodynamic stability for which theorem 1 is not applicable in its present form for the reasons just cited and which therefore cannot be brought under the present scheme of unification. The need for the establishment of an extended fundamental theorem in a framework which retains the essential character of the original one and at the same time can also account for such additional cases is a pressing one and Gupta et al (1985) have made significant contribution to the theory by giving a twist to the idea of 'representation' and successfully handling the resulting consequences of such a twist. Their work has extended the scope of the original theory by a considerable extent without sacrificing its elegant mathematical structure and in the following we describe their version of the fundamental theorem in all its essential points.…”