TY - JOUR

T1 - Orthogonality Relations for a Stationary Flow of an Ideal Fluid

AU - Sharafutdinov, V. A.

N1 - Publisher Copyright: © 2018, Pleiades Publishing, Ltd.

PY - 2018/7/1

Y1 - 2018/7/1

N2 - 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.

AB - 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.

KW - Euler equations

KW - ideal fluid

KW - integral momenta

KW - stationary flow

UR - http://www.scopus.com/inward/record.url?scp=85052988799&partnerID=8YFLogxK

U2 - 10.1134/S0037446618040158

DO - 10.1134/S0037446618040158

M3 - Article

AN - SCOPUS:85052988799

VL - 59

SP - 731

EP - 752

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 4

ER -