A third-order conservation law for the Kirchhoff-Pokhozhaev equation

2025/12/13 by Chiara Boiti, Boiti, Chiara, Renato Manfrin +1 · 2 citations
Engineering · Mathematics · Physics and Astronomy · #Stability and Controllability of Differential Equations #Navier-Stokes equation solutions #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2512.12380

Abstract

We prove that the special Kirchhoff equation studied by Pokhozhaev admits a third-order conservation law. We further show that if the energy of the solution is sufficiently small, then the L²-norms of the derivatives up to third order of the solution remain uniformly bounded with respect to time.

Cited by

• A Kirchhoff equation with infinite conservation laws
• Quasilinear normal form for the Kirchhoff-Poho\v zaev equation

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