| Abstract: | Quasi-linear integrodifferential equations that describe vortex flows of an ideal incomparessible liquid in a narrow curved
channel in the Eulerian-Lagrangian coordinate system are considered. The necessary and sufficient conditions for hyperbolicity
of the system of equations of motion are obtained for flows with a monotonic velocity depth profile. The propagation velocities
of the characteristics and the characteristic form of the system are calculated. A particular solution is given in which the
system of integrodifferential equations changes type with time. The solution of the Cauchy problem is given for linearized
equations. An example of initial data for which the Cauchy problem is ill-posed is constructed.
Novosibirsk State University, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39,
No. 4, pp. 38–49, July–August, 1998. |
