arXiv subjects

Simone Marrocco

Publications and source records attributed to Simone Marrocco.

2 recordsLinked to original sources

arXiv2026

On the integrability of the Kirchhoff-Pohozaev equation on tori

In this paper we study the Kirchhoff-Pohozaev equation introduced in \cite{P2} and its constants of motion (see \cite{BoitiManfrin2025}, \cite{BoitiManfrin2026}) on $n$ dimensional tori. We show that these Hamiltonians are all in involution and we prove that they are generated by an infinite list of constants of motion which are all defined and in involution on a fixed phase space. Then we study the Kirchhoff-Pohozaev equation restricted to a finite Fourier support. In dimension $n=1$ we show that such finite dimensional reduction is always completely integrable and provide an analytic Brikhoff normal form in a neighborhood of the origin. We also give sufficient conditions for integrability for $n>1$. We finally show that the formal Birkhoff Normal form of the Kirchhoff-Pohozaev equation is integrable for $n=1$.

math.DS↗

arXiv2026

Quasilinear normal form for the Kirchhoff-Poho{\v z}aev equation

On the $n$-dimensional torus $\mathbb{T}^n$, we consider the Kirchhoff-Poho{\v z}aev equation, which is the only Kirchhoff-type equation known to admit global solutions for small initial data in $H^s \times H^{s-1}$, $s \geq 2$. We study this equation from a dynamical perspective by means of a quasilinear normal form approach. We perform two steps of normal form reduction and show that the resulting cubic and quintic terms do not contribute to the Sobolev energy estimates. This cancellation reveals a special algebraic structure of the equation and represents a first step towards a dynamical explanation of its exceptional global well-posedness. As a further consequence, we obtain improved bounds on the growth of Sobolev norms and improved lower bounds on the existence time for initial data in $H^s \times H^{s-1}$ with $s \in [3/2, 2)$.

math.AP↗