Lp–Lq existence for the open compressible MHD system

Mostafa Meliani

doi:10.1016/j.na.2026.114057

Lp–Lq existence for the open compressible MHD system

Mostafa Meliani

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

We study the local existence of solutions to the Navier–Stokes–Fourier-magnetohydrodynamics (NSF-MHD) system describing the motion of a compressible, viscous, electrically and heat conducting fluid in the Lp–Lq class with inhomogeneous boundary conditions. The open system is allowed to receive incoming matter from the outside through (part of) the boundary which we refer to as an inflow boundary. This setup brings about a difficulty in estimating the regularity of the density ϱ which we remedy by assuming appropriate hypotheses on the velocity field, domain boundary and on the boundary and initial data of ϱ. The main result ensures the local well-posedness of the full NSF-MHD system which is shown through a linearization combined with a Banach fixed-point theorem.

Original language	English
Article number	114057
Journal	Nonlinear Analysis
Volume	267
Early online date	14 Jan 2026
DOIs	https://doi.org/10.1016/j.na.2026.114057
Publication status	E-pub ahead of print - 14 Jan 2026

Data Availability Statement

No data are associated with this article

Acknowledgements

The author is grateful to Prof. Eduard Feireisl (AVČR) for suggesting the topic of this manuscript and for his helpful discussions, and to Dr. Anna Abbatiello (U Campania) for helpful suggestions.

Funding

This work was carried out while the author was a postdoctoral researcher at the Institute of Mathematics of the Czech Academy of Sciences and was supported by the Czech Sciences Foundation (GAČR), Grant Agreement 24-11034S. The Institute of Mathematics of the Academy of Sciences of the Czech Republic is supported by RVO:67985840.

Funders	Funder number
Akademie Věd České Republiky
Grantová Agentura České Republiky	24-11034S
RVO	67985840

Keywords

Initial-boundary value problem
Local existence
Navier–Stokes–Fourier-MHD system
Strong solutions

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.na.2026.114057Licence: CC BY

Cite this

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AB - We study the local existence of solutions to the Navier–Stokes–Fourier-magnetohydrodynamics (NSF-MHD) system describing the motion of a compressible, viscous, electrically and heat conducting fluid in the Lp–Lq class with inhomogeneous boundary conditions. The open system is allowed to receive incoming matter from the outside through (part of) the boundary which we refer to as an inflow boundary. This setup brings about a difficulty in estimating the regularity of the density ϱ which we remedy by assuming appropriate hypotheses on the velocity field, domain boundary and on the boundary and initial data of ϱ. The main result ensures the local well-posedness of the full NSF-MHD system which is shown through a linearization combined with a Banach fixed-point theorem.

KW - Initial-boundary value problem

KW - Local existence

KW - Navier–Stokes–Fourier-MHD system

KW - Strong solutions

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JO - Nonlinear Analysis

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ER -

Lp–Lq existence for the open compressible MHD system

Abstract

Data Availability Statement

Acknowledgements

Funding

Keywords

ASJC Scopus subject areas

Access to Document

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