On the relation between decay and regularity of solutions to the modified Korteweg-de Vries equation

2023/04/22 by Muñoz, Alexander, Pastor, Ademir
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2304.11398

Abstract

This work is devoted to study the relation between the regularity index and the decay for solutions of the modified Korteweg-de Vries equation in weighted Sobolev spaces. We show if a solution belongs to a Sobolev space and has a large polynomial decay, compared to the regularity, then actually it is more regular than initially considered.

Related

• Long-time asymptotics of the modified KdV equation in weighted Sobolev spaces
• Propagation of regularity and decay of solutions to the k-generalized Korteweg-de Vries equation
• On the regularity of solutions to the k-generalized Korteweg-de Vries equation
• Exponential Decay Rates for the Damped Korteweg-de Vries Type Equation
• On the regularization mechanism for the periodic Korteweg-de Vries\n equation