The N-body problem, central to celestial mechanics and dynamical systems, explores the evolution and interaction of N objects under mutual forces—typically gravitational. Over decades, it has inspired ...

The Riemann problem for a two-dimensional hyperbolic system of pressureless gas dynamics equations is considered here. Riemann solutions are constructed for any piecewise-constant initial data having ...

The study of boundary value problems and optimal control in fluid dynamics constitutes a vital area in applied mathematics and engineering. These techniques form the foundation for formulating and ...