On the Growth in time of Sobolev Norms for Time Dependent Linear Generalized KdV-type Equations

2018/10/21 by Chengming Cao, Cao, Chengming, X.R. Yuan +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1810.08902

openalex publication_date 2018/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a detailed description in 1-D the growth of Sobolev norms for time dependent linear generalized KdV-type equations on the circle. For most initial data, the growth of Sobolev norms is polynomial in time for fixed analytic potential with admissible growth. If the initial data are given in a fixed smaller function space with more strict admissible growth conditions for V(x,t) , then the growth of previous Sobolev norms is at most logarithmic in time.

Related

• Logarithmic bounds on Sobolev norms for time-dependent linear Schrödinger equations
• Growth of Sobolev norms for abstract linear Schrödinger Equations
• Growth of Sobolev norms for linear Schrödinger operators
• Growth of Sobolev norms for unbounded perturbations of the Schrödinger equation on flat tori
• On the growth of Sobolev norms for a class of linear Schr "odinger\n equations on the torus with superlinear dispersion