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

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.

Keywords

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

2010 Mathematics Subject Classification

35-xx, 76Xxx

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Received 18 December 2021

Published 23 December 2022