3 papers
math.AP2026
Stability of dispersive boundary layers for scalar conservation laws in one space dimension
Paolo Antonelli, Pierangelo Marcati, Laura V. Spinolo
We study the zero-dispersion limit for a class of Korteweg--de Vries (KdV)-type initial-boundary value problems on the half-line, with Dirichlet boundary conditions assigned at \(x…
math.AP2026
The zero capillarity limit for the Euler-Korteweg system with no-flux boundary conditions
Paolo Antonelli, Yuri Cacchiò
In this article, we study the small dispersion limit of the Euler-Korteweg system in a domain with a smooth boundary and no-flux boundary conditions. We exploit a relative energy a…
math.AP2025
Global weak solutions of the Navier-Stokes-Korteweg Equations in one dimension
Paolo Antonelli, Didier Bresch, Stefano Spirito
We prove the global existence of weak solutions of the one-dimensional Navier-Stokes-Korteweg (NSK) equations when the viscosity and the capillarity coefficients are power function…