Analytic regularity for Navier-Stokes-Korteweg model on pseudo-measure spaces

TL;DR

This paper investigates the existence and analytic smoothing effects of the compressible Navier-Stokes system with quantum pressure in pseudo-measure spaces, introducing a new functional framework to handle non-linearities and control solutions point-wise.

Contribution

It provides improved bounds on the radius of analyticity and develops a novel approach using pseudo-measure spaces for PDE analysis.

Findings

Established existence and smoothing effects in pseudo-measure spaces.

Provided better lower bounds for the radius of analyticity.

Demonstrated the suitability of pseudo-measure spaces for nonlinear PDE control.

Abstract

The purpose of this work is to study the existence and analytic smoothing effect for the compressible Navier- Stokes system with quantum pressure in pseudo-measure spaces. This system has been considered by B. Haspot and an analytic smoothing effect for a Korteweg type system was considered by F. Charve, R. Danchin and J. Xu, both of them in Besov spaces. Here we give a better lower bound of the radius of analyticity near zero. This work is an opportunity to deepen the study of partial differential equations in pseudo-measure spaces by introducing a new functional setting to deal with non-linear terms. The pseudo-measure spaces are well-adapted to obtain a point-wise control of solutions, with to study of turbulence as perspective.