2025/10/30 by Boukarou, Aissa, Seghour, Lamia
#Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2510.26669
In this paper, we improve and extend the results obtained by Boukarou et al. \citeboukarou1 on the Gevrey regularity of solutions to a fifth-order Kadomtsev-Petviashvili-II equation. We establish Gevrey regularity in the time variable for solutions in 2+1 dimensions, providing a sharper result obtained through a new analytical approach. Assuming that the initial data are Gevrey regular of order σ≥ 1 in the spatial variables, we prove that the corresponding solution is Gevrey regular of order 5 σ in time. Moreover, we show that the function u(x, y, t), viewed as a function of t, does not belong to Gz for any 1 ≤ z<5 σ. Our proof introduces a new analytical method that establishes a general principle for dispersive equations of the form ∂t u = ±∂xαu + P(u), where ∂xα is the highest spatial derivative and P(u) a polynomial in spatial derivatives of total order at most α-1, the solution cannot belong to the Gevrey class Gz in time for any z satisfying 1 ≤ z<ασ.