The problem of forward motion of a hovercraft: asymptotic analysis of a solution

The linear unsteady problem describing the forward motion of a hovercraft with an oscillating forward velocity is considered. A two-term asymptotic representation of a solution is derived provided that the oscillation period is small. Estimates for the remainder in Sobolev spaces and some hydrodynamical consequences are also obtained. Bibliography: 17 titles. Illustrations: 1 figure. Dedicated to Nina Nikolaevna Uraltseva Translated from Problemy Matematicheskogo Analiza, 40, May 2009, pp. 91–104.