3 problems

Consider the one-dimensional general vacuum initial-value problem with initial sound speed satisfying $\bar c(x)\sim x^{1-\lambda}$ as $x\downarrow 0$, where $\lambda<0$. A local s…

Consider a one-dimensional isentropic Euler flow with fluid initially to the right of the origin, whose initial sound speed decays to zero like $x^{1-\lambda}$ as $x\downarrow 0$,…

Delta-shock conjecture. Delta-shocks are needed to resolve the Riemann problem with vacuum.