The global Gevrey regularity and analyticity of a two-component shallow water system with higher-order inertia operators

Abstract

In this paper, we mainly consider the Gevrey regularity and analyticity of the solution to a generalized two-component shallow water wave system with higher-order inertia operators, namely, m = (1 − ∂ 2x ) s u with s > 1. Firstly, we obtain the Gevrey regularity and analyticity for a short time. Secondly, we show the continuity of the data-to-solution map. Finally, we prove the global Gevrey regularity and analyticity in time.2010 Mathematics Subject Classification: 35Q53 (35B30 35B44 35C07 35G25)

Well-posedness and global solutions to the higher order Camassa-Holm equations with fractional inertia operator in Besov space

“…In [37], the authors established the localwellposedness in Besov spaces with lower-regularity, they also give the global solutions of (1.1) for the case a = 2, κ > 0. In [38], the authors study the local and global analyticity and Gevrey regularity of (1.1).…”

On the Cauchy problem for a four‐component Novikov system with peaked solutions

“…For more details with respect to peakons and wave breaking results of Equation (1.3), one can refer to [17][18][19][20][21] and the references therein. Due to the excellent structure of CH equation, a number of the mathematical properties of the solutions to the Cauchy problem associated with Equation (1.3) have been studied extensively, such as the local-well-posedness of the solutions [22][23][24][25], the nonuniformly continuous dependence on initial data of the solutions in Sobolev and Besov spaces [26][27][28][29], the persistence properties of the solutions [30], and the local and global Gevrey analyticity of the solutions [3,31].…”

“…The local well-posedness, global existence results, blow-up phenomenon of the solutions, the local and global Gevrey analytic solutions, and the nonuniform continuity of the solution map to the Cauchy problem associated with system (1.4) in Sobolev and Besov spaces have been studied by many scholars. For more details, one can refer to [3,31,[34][35][36][37][38] and references therein.…”