Dynamics of Partial Differential Equations

Volume 20 (2023)

Number 1

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

Pages: 1 – 21

DOI: https://dx.doi.org/10.4310/DPDE.2023.v20.n1.a1


A. Tendani Soler (Institut de Mathématiques, Université de Bordeaux, Talence, France)


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 improve the study of partial differential equations in pseudomeasure spaces by introducing a new functional setting to deal with non-linear terms. The pseudo-measure spaces are well-adapted to obtain a pointwise control of solutions, with a view to study turbulence.


analytic smoothing effects, compressible fluids, Navier–Stokes–Korteweg system, pseudo-measure spaces

2010 Mathematics Subject Classification

35-xx, 76Xxx

Received 18 December 2021

Published 23 December 2022