Universal structure of blow-up in 1D conservation laws
Mathematical Physics
2011-09-06 v1 math.MP
Fluid Dynamics
Abstract
We discuss universality properties of blow-up of a classical (smooth) solutions of conservation laws in one space dimension. It is shown that the renormalized wave profile tends to a universal function, which is independent both of initial conditions and of the form of a conservation law. This property is explained in terms of the renormalization group theory. A solitary wave appears in logarithmic coordinates of the Fourier space as a counterpart of this universality. Universality is demonstrated in two examples: Burgers equation and dynamics of ideal polytropic gas.
Keywords
Cite
@article{arxiv.1109.0662,
title = {Universal structure of blow-up in 1D conservation laws},
author = {Alexei A. Mailybaev},
journal= {arXiv preprint arXiv:1109.0662},
year = {2011}
}
Comments
8 pages, 2 figures