Analytical solutions to the pressureless Euler–Korteweg equations with free boundary
摘要
In this paper, we study the analytical solutions to the pressureless Euler–Korteweg equations. First, we construct a self-similar solution to the one-dimensional free boundary value problem with vacuum boundary condition and show that the free boundary spreads out linearly in time. Second, we extend this result to the N-dimensional radially symmetric case and the three-dimensional cylindrically symmetric case, respectively.