On Euler equation for incoherent fluid in curved spaces
Abstract
Hodograph equations for the Euler equation in curved spaces with constant pressure are discussed. It is shown that the use of known results concerning geodesics and associated integrals allows to construct several types of hodograph equations. These hodograph equations provide us with various classes of solutions of the Euler equation, including stationary solutions. Particular cases of cone and sphere in the 3-dimensional Eulidean space are analysed in detail. Euler equation on the sphere in the 4-dimensional Euclidean space is considered too.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.