On blow-up shock waves for a nonlinear PDE associated with Euler equations

Abstract

A second-order PDE is derived from Euler's equaitons under certain assumptions. It is shown that this PDE admits shock and rarefaction waves, and that a single point gradient blow-up admits a unique similarity extension after blow-up that settles uniqueness/entropy issues for such equations.

16 pages, 8 figures

References in corpus (5)

• Wave-breaking and generic singularities of nonlinear hyperbolic equations
• Formation of shocks in higher-order nonlinear dispersion PDEs: nonuniqueness and nonexistence of entropy
• Third-order nonlinear dispersion PDEs: shocks, rarefaction, and blow-up waves
• Nonlinear dispersion equations: smooth deformations, compactons, and extensions to higher orders
• Schock waves and compactons for fifth-order nonlinear dispersion equations. II