Orthogonality Relations for a Stationary Flow of an Ideal Fluid

Сибирский математический журнал

V. A. Sharafutdinov¹ 

[1] Novosibirsk State University

关键词: Euler equations;    stationary flow;    ideal fluid;    integral momenta;   

DOI  :  10.1134/S0037446618040158

学科分类：数学（综合）

来源: Izdatel stvo Instituta Matematiki Rossiiskoi Akademii Nauk

【 摘 要 】

For a real solution (u, p) to the Euler stationary equations for an ideal fluid, we derive an infinite series of the orthogonality relations that equate some linear combinations of mth degree integral momenta of the functions uiuj and p to zero (m = 0, 1,... ). In particular, the zeroth degree orthogonality relations state that the components ui of the velocity field are L2-orthogonal to each other and have coincident L2-norms. Orthogonality relations of degree m are valid for a solution belonging to a weighted Sobolev space with the weight depending on m.

【 授权许可】

CC BY