Loss of Regularity in the $K(m,n)$ Equations

Abstract

Using a priori estimates we prove that initially nonnegative, smooth and compactly supported solutions of the $K(m,n)$ equations must lose their smoothness in finite time. Formation of a singularity is a prerequisite for the emergence of compactons.

Cited by in corpus (2)

• Stability and interaction of compactons in the sublinear KdV equation
• Illposedness for dispersive equations: Degenerate dispersion and Takeuchi--Mizohata condition