A Simple Illustration of a Weak Spectral Cascade
A Simple Illustration of a Weak Spectral Cascade
The textbook first encounter with nonlinearity in a partial differential equation (PDE) is the first-order wave equation: $u_t + u u_x = 0$. Often referred to as the inviscid Burgers equation, this equation is familiar to many in the theoretical contexts of characteristics, wavebreaking, or shock propagation. Another canonical behavior …