Ideal incompressible fluid motion in domains with edges. I (Q1082933)

The author considers the transient Euler equations for a bounded domain in \({\mathbb{R}}^ 3\) with impermeable walls whose tangential velocity is prescribed. A forcing term is admitted in the equations of motion. Whereas existence and uniqueness of solutions is well known in the case of smooth boundaries, he shows regularity properties of solutions in neighborhoods of edges. By use of alternative approaches, he establishes two upper bounds for the angle defining the edge. The proofs (in weighted Sobolev spaces) are confined to sufficiently small intervals of time. The proofs employ sequences of well-posed auxiliary problems and pertain to weakly convergent successive approximations. Details of proofs are omitted.