Special Session 76: Recent Developments in Nonlinear and Nonlocal Evolution Equations

Singularity formation and global weak solutions to the Serre-Green-Naghdi equations with surface tension

Billel Guelmame
ENS Lyon
France
Co-Author(s):    
Abstract:
In this talk, we explore the Serre-Green-Naghdi equations, which describe shallow-water waves while considering the influence of surface tension. These equations are locally (in time) well-posed. We identify a class of smooth initial data, leading to the development of singularities in finite time for the corresponding strong solutions. Additionally, we demonstrate the existence of global weak solutions for small-energy initial data.