2 problems

Let $\mathbf{u}$ be the velocity field on the $d$-dimensional torus, let $\hat{\mathbf{u}}(\mathbf{n})$ denote its Fourier coefficients, and let $\nu>0$ be the viscosity. For a wav…

Consider the potential Burgers equation in the small-viscosity regime $0<\nu\ll 1$, with Fourier coefficients $\hat{u}(k)$ of the solution. For moderately large wavenumbers $k$, co…