A continuum of invariant measures for the periodic KdV and mKdV equations

2023/05/23 by Andreia Chapouto, Chapouto, Andreia, Justin Forlano +1
Environmental Science · Mathematics · Physics and Astronomy · #35Q53 #35Q55 #60H30 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Hydrology and Drought Analysis #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2305.14565

openalex publication_date 2023/05/23 · openalex created_date 2023/05/27 · openalex updated_date 2026/07/28

Abstract

We consider the real-valued defocusing modified Korteweg-de Vries equation (mKdV) on the circle. Based on the complete integrability of mKdV, Killip-Vişan-Zhang (2018) discovered a conserved quantity which they used to prove low regularity a priori bounds for solutions. It has been an open question if this conserved quantity can be used to define invariant measures supported at fractional Sobolev regularities. Motivated by this question, we construct probability measures supported on H^s(\mathbbT) for 0

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