Hydrodynamic limit of the Kuramoto-Sakaguchi equation with inertia and noise effects

2024/10/07 by Mai, Tina
#34C15 #35Q35 #35Q70 #35Q84 #92B25 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2410.05113

Abstract

We consider the Kuramoto-Sakaguchi-Fokker-Planck equation (namely, parabolic Kuramoto-Sakaguchi, or Kuramoto-Sakaguchi equation, which is a nonlinear parabolic integro-differential equation) with inertia and white noise effects. We study the hydrodynamic limit of this Kuramoto-Sakaguchi equation. During showing this main result, as a support, we also prove a Hardy-type inequality over the whole real line.

Related

• Trend to equilibrium and diffusion limit for the inertial Kuramoto-Sakaguchi equation
• Asymptotic stability of the phase-homogeneous solution to the Kuramoto-Sakaguchi equation with inertia
• New bounds for the inhomogenous Burgers and the Kuramoto-Sivashinsky equations
• Toward a quantitative theory of the hydrodynamic limit
• Hydrodynamic noise in one dimension: projected Kubo formula and how it vanishes in integrable models