arXiv subjects

Adrien Tendani Soler

Publications and source records attributed to Adrien Tendani Soler.

2 recordsLinked to original sources

arXiv2024

Local exact controllability to constant trajectories for Navier-Stokes-Korteweg model

In this article, we study the local exact controllability to a constant trajectory for a compressible Navier-Stokes-Korteweg system on the torus in dimension $ d\in\{1,2,3\}$ when the control acts on an open subset. To be more precise, we obtain the local exact controllability to the constant state $(ρ_{\star},0)$ for arbitrary small positive times and without any geometric condition on the control region. In order to do so, we analyze the control properties of the linearized equation, and present a detailed study of the observability of the adjoint equations. In particular, we shall exhibit the parabolic (possibly also dispersive) structure of these adjoint equations. Based on that, we will be able to recover observability of the adjoint system through Carleman estimates.

math.AP↗

arXiv2022

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 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.

math.AP↗