14 citations · 25 across the 18 of their papers we have counts for
19 papers
Uniform Decay for Ruggeri's Relaxed Navier-Stokes-Fourier Equations
Heinrich Freistühler, Yizhou Zhou
This work studies the linearization of Ruggeri's classical symmetric hyperbolic model of viscous, heat-conductive fluids about a homogeneous equilibrium. In three space dimensions,…
Dynamical stability of planar phase boundaries for hyperelastic materials of Hadamard type
Heinrich Freistühler, Lauro Morales, Ramón G. Plaza +1
The dynamical stability of laminates or planar phase boundaries for hyperelastic materials of Hadamard type in two space dimensions is studied. For that purpose, the stability func…
Consistency of some well-posed five-field theories of dissipative relativistic fluid dynamics
Heinrich Freistuhler
Within the FTBDNK family of formulations of relativistic Navier-Stokes (H. Freistühler and B. Temple, Proc. R. Soc. A 470, 20140055 (2014), Proc. R. Soc. A 473 (2017), 20160729; F.…
Linear Degeneracy in a Class of Nonlinear Second-Order Hyperbolic Systems
Heinrich Freistuhler
For a class of nonlinear hyperbolic systems of second order the paper shows that all Lax modes associated with their first-order formulations are linearly degenerate. This property…
On Phase Boundaries in Relativistic Korteweg Fluids
Heinrich Freistuhler
This is the first of several planned papers that study the existence and local-in-time persistence of phase fronts in the Lorentz invariant Euler equations for gases of van der Waa…
Formation of Singularities in Solutions to Ruggeri's Hyperbolic Navier-Stokes Equations
Heinrich Freistuhler
Ruggeri's hyperbolic Navier-Stokes equations are shown to possess, for any equilibrium state, smooth solutions in arbitrarily small neigborhoods of the reference state t…
On Shock Profiles in Four-Field Formulations of Dissipative Relativistic Fluid Dynamics
Heinrich Freistuhler
This paper shows that in second-order hyperbolic systems of partial differential equations proposed in authors' earlier paper (J. Math. Phys. 59 (2018)) for modelling the relativis…
A Causal Formulation of Dissipative Relativistic Fluid Dynamics with or without Diffusion
Heinrich Freistuhler
The article proposes a causal five-field formulation of dissipative relativistic fluid dynamics as a quasilinear symmetric hyperbolic system of second order. The system is determin…
Remarks on Ruggeri's First Model of Dissipative Fluid Dynamics as a Symmetric Hyperbolic System
Heinrich Freistuhler
This note establishes properties of a model of dissipative fluid dynamics as a symmetric hyperbolic system by which Ruggeri once triggered the development of Rational Extended Ther…
A Galilei Invariant Version of Yong's Model
Heinrich Freistuhler
In a paper in Arch. Rational Mech. 214 (2014), Wen-An Yong has described the dynamics of a compressible fluid with Maxwell delayed viscosity as a symmetric hyperbolic system of bal…
The Blesgen and Lowengrub-Truskinovsky Descriptions of Two-Phase Compressible Fluid Flow: Interstitial Working and a Reduction to Korteweg Theory
Heinrich Freistühler, Matthias Kotschote
Formulated by Blesgen and Lowengrub and Truskinovsky, the `Navier-Stokes-Allen-Cahn' (NSAC) equations and the `Navier-Stokes-Cahn-Hilliard' (NSCH) equations describe diphasic fluid…
Godunov Variables in Relativistic Fluid Dynamics
Heinrich Freistuhler
This note presents Godunov variables and 4-potentials for the relativistic Euler equations of barotropic fluids. The associated additional conservation/ production law has differen…
Emergence of Unstable Modes for Shock Waves in Ideal MHD
Heinrich Freistuhler, Felix Kleber, Johannes Schropp
This note studies classical magnetohydrodynamic shock waves in an inviscid fluidic plasma that is assumed to be a perfect conductor of heat as well as of electricity. For this math…
Reductions of the Navier-Stokes-Allen-Cahn and the Navier-Stokes-Cahn-Hilliard equations
Heinrich Freistuhler, Matthias Kotschote
This paper studies two well-known models for two-phase fluid flow at constant temperature, the isothermal Navier-Stokes-Allen-Cahn and the isothermal Navier-Stokes-Cahn-Hilliard eq…
Diffuse planar phase boundaries in a two-phase fluid with one very dense phase
Heinrich Freistuhler, Matthias Kotschote
This note studies Navier-Stokes-Allen-Cahn models for compressible fluids that are mixtures of two incompressible phases whose density ratio eps=rho_1/rho_2 is very small. Under a…
Diffuse planar phase boundaries in a two-phase fluid with one incompressible phase
Heinrich Freistuhler, Matthias Kotschote
This note studies a family of Navier-Stokes-Allen-Cahn systems parameterized by temperature. Derived from an internal energy that corresponds to one incompressible and one compress…
An analytical proof for the stability of Heimburg-Jackson pulses
Heinrich Freistühler, Johannes Höwing
This paper studies analytically the stability of solitary waves in a generalized Boussinesq equation with quadratic-cubic nonlinearity. For general values of two parameters a and b…
Symmetrizations of RMHD equations and stability of relativistic current-vortex sheets
Heinrich Freistühler, Yuri Trakhinin
We consider the equations of relativistic magnetohydrodynamics (RMHD) in the case of special relativity. For the fluid rest frame a nonconservative reformulation of the RMHD equati…
The Lopatinski determinant of small shocks may vanish
Heinrich Freistuhler, Peter Szmolyan
The Kreiss-Majda Lopatinski determinant encodes a uniform stability property of shock wave solutions to hyperbolic systems of conservation laws in several space variables. This not…