Report
THE EQUATIONS OF EXTENDED MAGNETOHYDRODYNAMICS ; Les équations de la magnétohydrodynamique étendue
| العنوان: | THE EQUATIONS OF EXTENDED MAGNETOHYDRODYNAMICS ; Les équations de la magnétohydrodynamique étendue |
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| المؤلفون: | Cheverry, Christophe, Besse, Nicolas |
| المساهمون: | Institut de Recherche Mathématique de Rennes (IRMAR), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), Observatoire de la Côte d'Azur (OCA), Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS) |
| المصدر: | https://hal.science/hal-04622238 ; 2024. |
| بيانات النشر: | HAL CCSD |
| سنة النشر: | 2024 |
| المجموعة: | Archive Ouverte de l'Université Rennes (HAL) |
| مصطلحات موضوعية: | Hyperbolic-parabolic symmetric systems of conservation laws, Initial value problem for nonlinear systems of PDEs, Partially elliptic systems, Compressible and incompressible fluid mechanics, Plasma physics, Hall, Inertial and Extended Magnetohydrodynamics, Pseudo-differential operators, Hyperbolic-parabolic symmetric systems of conservation laws Initial value problem for nonlinear systems of PDEs Partially elliptic systems Compressible and incompressible fluid mechanics Plasma physics Hall, Inertial and Extended Magnetohydrodynamics Pseudo-differential operators Weyl quantization, Weyl quantization, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] |
| Time: | 35 |
| الوصف: | Extended magnetohydrodynamics (XMHD) is a fluid plasma model generalizing ideal MHD by taking into account the impact of Hall drift effects and the influence of electron inertial effects. XMHD has a Hamiltonian structure which has received over the past ten years a great deal of attention among physicists, and which is embodied by a non canonical Poisson algebra on an infinite-dimensional phase space. XMHD can alternatively be formulated as a nonlinear evolution equation. Our aim here is to investigate the corresponding Cauchy problem. We consider both incompressible and compressible versions of XMHD with, in the latter case, some additional bulk (fluid) viscosity. In this context, we show that XMHD can be recast as a well-posed symmetric hyperbolic-parabolic system implying pseudo-differential operators of order zero acting as coefficients and source terms. Along these lines, we can solve locally in time the associated initial value problems, with moreover a minimal Sobolev regularity. We also explain the emergence and propagation of inertial waves. |
| نوع الوثيقة: | report |
| اللغة: | English |
| Relation: | info:eu-repo/semantics/altIdentifier/arxiv/2406.17356; ARXIV: 2406.17356 |
| الاتاحة: | https://hal.science/hal-04622238 https://hal.science/hal-04622238v1/document https://hal.science/hal-04622238v1/file/XMHD-19-06.pdf |
| Rights: | info:eu-repo/semantics/OpenAccess |
| رقم الانضمام: | edsbas.D38EDF4F |
| قاعدة البيانات: | BASE |
| الوصف غير متاح. |