A class of solutions for self‐gravitating dust in Newtonian gravity

摘要: The Lagrange method is used to obtain a class of solutions the three‐dimensional hydrodynamical equations governing motion matter with vanishing pressure in its own Newtonian gravitational field. characterized by property that each fluid particle has constant acceleration. contains rotational and irrotational flows. For flows expansion tensor one zero eigenvalue, while for it two eigenvalues, which implies every element contracts or expands spatial directions, respectively; nevertheless, density depends on all three coordinates. general one‐dimensional solution included as subclass.