A system of partial differential equations models the magneto-hydrodynamics of an ideal fluid in a bounded time-space domain Q = (0, τ ) × BR [⃗0] endowed with EUCLIDean metric and having M=3 space dimensions. The equations describe conservation of mass, conservation of momentum and magnetic induction. The {mass, momentum} equations correspond to the {time, space} divergence (Div[·]) of a 4 × 4 tensor denoted AEULER, which is real valued, symmetric and positive definite, provided the terms depending on the magnetic field, H⃗ , are moved to the right side. By assuming the existence of a solution to some initial-boundary value problem, a property known as the “higher integrability” of det[AEULER] is investigated. Articles by D. SERRE from 2018 onwards [Divergence-free positive symmetric tensors and fluid dynamics. Ann. I. H. Poincare ́ - Analyse Non-lin.. 2018;AN 35:1209-1234] motivated this work. Letting Φ := p + ρf φ, with p pressure, ρf density and φ (>0) the potential of external forces, one has det[AEULER] = ΦMρf. If the entries of AEULER are in L1(Q), then higher integrability consists of ρ1/MΦ ∈ L1(Q) and holds provided Div[AEULER] has finite total mass in Q. Higher integrability thus affects p and ρf , leaving out velocity, ⃗u, and H⃗ . If a solution {ρf , p, ⃗u, H⃗ } were known to exist and comply with a number of requirements, then higher integrability would mean continuous dependence of ρ1/M Φ on H⃗ . In the absence of information about existence, the L1 (Q)-estimate is a qualitative result about the dynamical system: a property of the solution is inferred from that of det[AEULER]. Many problems are still open, some of which are stated.
Crosta, G. (2022). Higher integrability of a determinant related to a system of magneto-hydrodynamics [Working paper].
Citazione: | Crosta, G. (2022). Higher integrability of a determinant related to a system of magneto-hydrodynamics [Working paper]. | |
Titolo: | Higher integrability of a determinant related to a system of magneto-hydrodynamics | |
Autori: | Crosta, G | |
Autori: | ||
Presenza di un coautore afferente ad Istituzioni straniere: | No | |
Carattere della pubblicazione: | Scientifica | |
DCMI: | Working paper | |
Data di pubblicazione: | 2022 | |
Descrizione del prodotto (Altro): | Versione nel formato documentclass{article} e con bibliografia ibliographystyle{spiebib} di un capitolo accettato per la pubblicazione. | |
Altre informazioni: | Sorgente LaTEX: documentclass{article}. Pacchetti significativi di formatazione: usepackage{amsthm}, usepackage{quoting}. Stile bibliografico: bibliographystyle{spiebib}. Compilatore: TeXShop Version 4.01 (4.01). PDF: 1.5. Produttore del PDF: pdfTeX-1.40.13. Creatore del contenuto: TeX. | |
Lingua: | English | |
Sostituisce: | http://hdl.handle.net/10281/360678 Higher integrability of a determinant related to a system of magneto-hydrodynamic equations | |
Appare nelle tipologie: | 99 - Altro |
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