Advancements in Gevrey Regularity for a Coupled Kadomtsev–Petviashvili II System: New Insights and Findings

Abstract

In this work, we prove that the initial value problem for a system of two Kadomtsev–Petviashvili II (KP II) equations coupled via both dispersive and nonlinear terms is locally well-posed in anisotropic Gevrey spaces Gs1,s2δ1,δ2,ϱ(R2)×Gs1,s2δ1,δ2,ϱ(R2) with −1/3<s1<0 and s2≥0. This advancement extends recent findings regarding the well-posedness of this model within anisotropic Sobolev spaces Hs1,s2(R2)×Hs1,s2(R2). The current strategy is based on both linear and nonlinear estimates. Additionally, to further explore the system’s temporal behavior, we establish that Gevrey regularity of order 3ρ (or simply Gevrey—3ρ regularity in time) exists.