Details of Grant 

EPSRC Reference:	GR/S96609/02
Title:	Ideal and Dissapative Stability of Shock Fronts in Magnetohydrodynamics
Principal Investigator:	Ilin, Dr K
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Researcher Co-Investigators:
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Department:	Mathematics
Organisation:	University of York
Scheme:	Standard Research (Pre-FEC)
Starts:	01 February 2006	Ends:	30 June 2007	Value (£):	4,850
EPSRC Research Topic Classifications:	Continuum Mechanics Plasmas - Laser & Fusion
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
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Panel History:
Summary on Grant Application Form
Plasma flows with shock waves are often observed in astrophysical phenomena. Such flows can be described using mathematical models based on the equations of compressible magnetohydrodynamics (MHD), and various MHD models have successfully reproduced many aspects of the observations, for example, for flows around planets, moons, comets, when so-called bow shocks are generated in front of these space objects. At the same time, shock waves, being formally introduced within the framework of a mathematical model, sometimes do not exist in the real physical world. The topic of the proposed research is to study the existence of shock fronts in MHD plasmas. The proposed research consists of two main parts that are closely connected. The aim of the first part is to find conditions for existence (stability) and non-existence (instability) of MHD shock waves that are viewed as surfaces of strong discontinuity for the model of compressible MHD without dissipation (i.e. for inviscid perfectly conducting fluids). The stability of so-called rotational discontinuities, which are important for certain astrophysical applications, will be also investigated. We propose to study the stability of MHD shock discontinuities and rotational discontinuities using both analytical and numerical methods, and in linear and nonlinear statement. The second part of proposed research is devoted to the dissipative (or viscous) stability of MHD shock waves. Here, we propose to obtain conditions for linearized stability and instability of viscous profiles (structures) of MHD shock waves, at least, for some particular classes of shocks, with the emphasis on shocks for which the 'ideal' (discontinuous) approximation does not answer the question about their real existence.
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