Stability of an incompressible plasma–vacuum interface with displacement current in vacuum

Standard

Stability of an incompressible plasma–vacuum interface with displacement current in vacuum. / Morando, Alessandro; Secchi, Paolo; Trakhinin, Yuri et al.

In: Mathematical Methods in the Applied Sciences, Vol. 43, No. 12, 01.08.2020, p. 7465-7483.

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

Harvard

Morando, A, Secchi, P, Trakhinin, Y & Trebeschi, P 2020, 'Stability of an incompressible plasma–vacuum interface with displacement current in vacuum', Mathematical Methods in the Applied Sciences, vol. 43, no. 12, pp. 7465-7483. https://doi.org/10.1002/mma.6488

APA

Morando, A., Secchi, P., Trakhinin, Y., & Trebeschi, P. (2020). Stability of an incompressible plasma–vacuum interface with displacement current in vacuum. Mathematical Methods in the Applied Sciences, 43(12), 7465-7483. https://doi.org/10.1002/mma.6488

Vancouver

Morando A, Secchi P, Trakhinin Y, Trebeschi P. Stability of an incompressible plasma–vacuum interface with displacement current in vacuum. Mathematical Methods in the Applied Sciences. 2020 Aug 1;43(12):7465-7483. doi: 10.1002/mma.6488

Author

Morando, Alessandro ; Secchi, Paolo ; Trakhinin, Yuri et al. / Stability of an incompressible plasma–vacuum interface with displacement current in vacuum. In: Mathematical Methods in the Applied Sciences. 2020 ; Vol. 43, No. 12. pp. 7465-7483.

BibTeX

@article{4f125e8fc443421695f889593238de27,

title = "Stability of an incompressible plasma–vacuum interface with displacement current in vacuum",

abstract = "We study the free boundary problem for a plasma–vacuum interface in ideal incompressible magnetohydrodynamics. Unlike the classical statement when the vacuum magnetic field obeys the div-curl system of pre-Maxwell dynamics, to better understand the influence of the electric field in vacuum, we do not neglect the displacement current in the vacuum region and consider the Maxwell equations for electric and magnetic fields. Under the necessary and sufficient stability condition for a planar interface found earlier by Trakhinin, we prove an energy a priori estimate for the linearized constant coefficient problem. The process of derivation of this estimate is based on various methods, including a secondary symmetrization of the vacuum Maxwell equations, the derivation of a hyperbolic evolutionary equation for the interface function, and the construction of a degenerate Kreiss-type symmetrizer for an elliptic-hyperbolic problem for the total pressure.",

keywords = "degenerate Kreiss' symmetrizer, Fourier transform, ideal incompressible magnetohydrodynamics, linearized stability, Maxwell equations, plasma–vacuum interface, plasma-vacuum interface, WELL-POSEDNESS",

author = "Alessandro Morando and Paolo Secchi and Yuri Trakhinin and Paola Trebeschi",

year = "2020",

month = aug,

day = "1",

doi = "10.1002/mma.6488",

language = "English",

volume = "43",

pages = "7465--7483",

journal = "Mathematical Methods in the Applied Sciences",

issn = "0170-4214",

publisher = "John Wiley and Sons Ltd",

number = "12",

}

RIS

TY - JOUR

T1 - Stability of an incompressible plasma–vacuum interface with displacement current in vacuum

AU - Morando, Alessandro

AU - Secchi, Paolo

AU - Trakhinin, Yuri

AU - Trebeschi, Paola

PY - 2020/8/1

Y1 - 2020/8/1

N2 - We study the free boundary problem for a plasma–vacuum interface in ideal incompressible magnetohydrodynamics. Unlike the classical statement when the vacuum magnetic field obeys the div-curl system of pre-Maxwell dynamics, to better understand the influence of the electric field in vacuum, we do not neglect the displacement current in the vacuum region and consider the Maxwell equations for electric and magnetic fields. Under the necessary and sufficient stability condition for a planar interface found earlier by Trakhinin, we prove an energy a priori estimate for the linearized constant coefficient problem. The process of derivation of this estimate is based on various methods, including a secondary symmetrization of the vacuum Maxwell equations, the derivation of a hyperbolic evolutionary equation for the interface function, and the construction of a degenerate Kreiss-type symmetrizer for an elliptic-hyperbolic problem for the total pressure.

AB - We study the free boundary problem for a plasma–vacuum interface in ideal incompressible magnetohydrodynamics. Unlike the classical statement when the vacuum magnetic field obeys the div-curl system of pre-Maxwell dynamics, to better understand the influence of the electric field in vacuum, we do not neglect the displacement current in the vacuum region and consider the Maxwell equations for electric and magnetic fields. Under the necessary and sufficient stability condition for a planar interface found earlier by Trakhinin, we prove an energy a priori estimate for the linearized constant coefficient problem. The process of derivation of this estimate is based on various methods, including a secondary symmetrization of the vacuum Maxwell equations, the derivation of a hyperbolic evolutionary equation for the interface function, and the construction of a degenerate Kreiss-type symmetrizer for an elliptic-hyperbolic problem for the total pressure.

KW - degenerate Kreiss' symmetrizer

KW - Fourier transform

KW - ideal incompressible magnetohydrodynamics

KW - linearized stability

KW - Maxwell equations

KW - plasma–vacuum interface

KW - plasma-vacuum interface

KW - WELL-POSEDNESS

UR - http://www.scopus.com/inward/record.url?scp=85084508308&partnerID=8YFLogxK

U2 - 10.1002/mma.6488

DO - 10.1002/mma.6488

M3 - Article

AN - SCOPUS:85084508308

VL - 43

SP - 7465

EP - 7483

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

SN - 0170-4214

IS - 12

ER -

ID: 24259995