On a third order initial boundary value problem in a plane domain

Abstract

Third order initial boundary value problem is studied in a bounded plane domain σ with C⁴ smooth boundary ∂σ. The existence and uniqueness of the solution is proved using Galerkin approximations and a priory estimates. The problem under consideration appear as an auxiliary problem by studying a second grade fluid motion in an infinite three-dimensional pipe with noncircular cross-section.