scholarly journals The Riemann problem admitting δ-, δ′-shocks, and vacuum states (the vanishing viscosity approach)

2006 ◽  
Vol 231 (2) ◽  
pp. 459-500 ◽  
Author(s):  
V.M. Shelkovich
Keyword(s):  
Riemann Problem ◽  
Vanishing Viscosity ◽  
Vacuum States

scholarly journals Pressureless Magnetohydrodynamics System: Riemann Problem and Vanishing Magnetic Field Limit

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Shiwei Li ◽  
Hongjun Cheng ◽  
Hanchun Yang
Keyword(s):  
Magnetic Field ◽  
Riemann Problem ◽  
Vacuum State ◽  
Riemann Solutions ◽  
Delta Shock ◽  
Vacuum States ◽  
Mhd System ◽  
Delta Shocks ◽  
The Magnetic Field ◽  
Intermediate Density

This paper proposes the pressureless magnetohydrodynamics (MHD) system by neglecting the effect of pressure difference in the MHD system. Firstly, the Riemann problem for the pressureless MHD system is solved with five kinds of structures of solutions consisting of combinations of shock, rarefaction wave, contact discontinuity, and vacuum state. Secondly, the limit behavior of the obtained Riemann solutions as the magnetic field drops to zero is studied. It is shown that, as the magnetic field vanishes, the Riemann solutions of the pressureless MHD system just tend to the corresponding Riemann solutions of the Euler equations for pressureless fluids. The formation processes of delta shocks and vacuum states are clarified. For the delta shock, both the intermediate density and internal energy simultaneously develop delta measures.

STABILITY OF RAREFACTION WAVES AND VACUUM STATES FOR THE MULTIDIMENSIONAL EULER EQUATIONS

2007 ◽  
Vol 04 (01) ◽  
pp. 105-122 ◽  
Author(s):  
GUI-QIANG CHEN ◽  
JUN CHEN
Keyword(s):  
Initial Data ◽  
Large Class ◽  
Euler Equations ◽  
Riemann Problem ◽  
Global Attractors ◽  
Compressible Fluids ◽  
Entropy Solutions ◽  
Rarefaction Waves ◽  
One Dimensional ◽  
Vacuum States

We are interested in properties of the multidimensional Euler equations for compressible fluids. Rarefaction waves are the unique solutions that may contain vacuum states in later time, in the context of one-dimensional Riemann problem, even when the Riemann initial data are away from the vacuum. For the multidimensional Euler equations describing isentropic or adiabatic fluids, we prove that plane rarefaction waves and vacuum states are stable within a large class of entropy solutions that may contain vacuum states. Rarefaction waves and vacuum states are also shown to be global attractors of entropy solutions in L∞, provided initial data are L∞ ∩ L1 perturbations of Riemann initial data. Our analysis applies to entropy solutions with arbitrarily large oscillation, and no bounded variation regularity is required.

Vanishing viscosity limit for Riemann solutions to a 2 × 2 hyperbolic system with linear damping

2021 ◽  
pp. 1-22
Author(s):  
Richard De la cruz ◽  
Juan Juajibioy
Keyword(s):  
Conservation Laws ◽  
Riemann Problem ◽  
Existence Of Solutions ◽  
Time Dependent ◽  
Viscosity Method ◽  
Vanishing Viscosity ◽  
Riemann Solutions ◽  
Vanishing Viscosity Limit ◽  
Viscosity Limit ◽  
Linear Damping

In this paper, we propose a time-dependent viscous system and by using the vanishing viscosity method we show the existence of solutions for the Riemann problem to a particular 2 × 2 system of conservation laws with linear damping.

scholarly journals Covariant phase space and soft factorization in non-Abelian gauge theories

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Temple He ◽  
Prahar Mitra
Keyword(s):  
Phase Space ◽  
Ward Identity ◽  
Gauge Theories ◽  
Minkowski Spacetime ◽  
Soft Gluon ◽  
Careful Study ◽  
Abelian Gauge ◽  
Gauge Sector ◽  
Vacuum States ◽  
The One

Abstract We perform a careful study of the infrared sector of massless non-abelian gauge theories in four-dimensional Minkowski spacetime using the covariant phase space formalism, taking into account the boundary contributions arising from the gauge sector of the theory. Upon quantization, we show that the boundary contributions lead to an infinite degeneracy of the vacua. The Hilbert space of the vacuum sector is not only shown to be remarkably simple, but also universal. We derive a Ward identity that relates the n-point amplitude between two generic in- and out-vacuum states to the one computed in standard QFT. In addition, we demonstrate that the familiar single soft gluon theorem and multiple consecutive soft gluon theorem are consequences of the Ward identity.

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