Solvability of an initial boundary value problem for the euler equations in twodimensional domain with corners
作者:
W. M. Zajaczkowski,
A. Piskorek,
期刊:
Mathematical Methods in the Applied Sciences
(WILEY Available online 1984)
卷期:
Volume 6,
issue 1
页码: 1-22
ISSN:0170-4214
年代: 1984
DOI:10.1002/mma.1670060102
出版商: John Wiley&Sons, Ltd
数据来源: WILEY
摘要:
AbstractThe aim of this paper is to prove the existence and uniqueness of local solutions of some initial boundary value problems for the Euler equations of an incompressible fluid in a bounded domain Ω ⊂R2with corners. We consider two cases of a nonvanishing normal component of velocity on the boundary. In three‐dimensional case such problems have been considered in papers [12], [13], [14]. Similar problems in domains without corners have been considered in [2]–[6], [11]. In this paper the relation between the maximal corner angle of the boundary and the smoothness of the solutions is shown. The paper consists of four sections. In section 1 two initial boundary value problems for the Euler equations are formulated. In section 2 the existence and uniqueness of solutions of the Laplace equation in twodimensional domain with corners for the Dirichlet and Neumann problems is proved in the Sobolev spaces. In sections 3 and 4 we prove the existence and uniqueness of solutions of problems formulated in section 1, using the method of successive approxim
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