Singularity Formation in the Inviscid Burgers Equation

Abstract

We provide a lower bound for the blow up time of the H2 norm of the entropy solutions of the inviscid Burgers equation in terms of the H2 norm of the initial datum. This shows an interesting symmetry of the Burgers equation: the invariance of the space H2 under the action of such nonlinear equation. The argument is based on a priori estimates of energy and stability type for the (viscous) Burgers equation.

Keywords

• existence
• uniqueness
• stability
• Burgers equation
• Cauchy problem