Athanasios E. Tzavaras
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View article: Asymptotic limits for strain-gradient viscoelasticity with nonconvex energy
Asymptotic limits for strain-gradient viscoelasticity with nonconvex energy Open
We consider the system of viscoelasticity with higher-order gradients and nonconvex energy in several space dimensions. We establish the asymptotic limits when the viscosity or when the dispersion coefficient . For the latter pro…
View article: Absence of anomalous dissipation for weak solutions of the Maxwell–Stefan system
Absence of anomalous dissipation for weak solutions of the Maxwell–Stefan system Open
In this paper we give a short and self-contained proof of the fact that weak solutions to the Maxwell–Stefan system automatically satisfy an entropy equality, establishing the absence of anomalous dissipation.
View article: Analytic solutions for Vlasov equations with nonlinear zero-moment dependence
Analytic solutions for Vlasov equations with nonlinear zero-moment dependence Open
We consider nonlinear Vlasov-type equations involving powers of the zero-order moment and obtain a local existence and uniqueness result within a framework of analytic functions. The proof employs a Banach fixed point argument, where a con…
View article: Asymptotic Limits for Strain-Gradient Viscoelasticity with Nonconvex Energy
Asymptotic Limits for Strain-Gradient Viscoelasticity with Nonconvex Energy Open
We consider the system of viscoelasticity with higher-order gradients and nonconvex energy in several space dimensions. We establish the asymptotic limits when the viscosity $ν\rightarrow 0$ or when the dispersion coefficient $δ\rightarrow…
View article: A bilinear fractional integral operator for Euler-Riesz systems
A bilinear fractional integral operator for Euler-Riesz systems Open
We establish a uniform estimate for a bilinear fractional integral operator via restricted weak-type endpoint estimates and Marcinkiewicz interpolation. This estimate is crucial in the integrability analysis of a tensor-valued bilinear fra…
View article: Strong convergence of sequences with vanishing relative entropy
Strong convergence of sequences with vanishing relative entropy Open
We show that under natural growth conditions on the entropy function, convergence in relative entropy is equivalent to $L_p$-convergence. The main tool is the theory of Young measures, in a form that accounts for the formation of concentra…
View article: Absence of anomalous dissipation for weak solutions of the Maxwell--Stefan system
Absence of anomalous dissipation for weak solutions of the Maxwell--Stefan system Open
In this paper we give a short and self-contained proof of the fact that weak solutions to the Maxwell-Stefan system automatically satisfy an entropy equality, establishing the absence of anomalous dissipation.
View article: Oscillations in Compressible Navier-Stokes and Homogenization in Phase Transition problems
Oscillations in Compressible Navier-Stokes and Homogenization in Phase Transition problems Open
In the first part of this article we present some exact solutions for special hyperbolic-parabolic systems with sustained oscillations induced by the initial data, most notably the compressible Navier-Stokes system with non-monotone pressu…
View article: Sustained Oscillations in Hyperbolic-Parabolic Systems
Sustained Oscillations in Hyperbolic-Parabolic Systems Open
We construct examples of oscillating solutions with persistent oscillations for various hyperbolic-parabolic systems with singular diffusion matrices that appear in mechanics. These include, an example for the equations of nonlinear viscoe…
View article: Oscillatory and regularized shock waves for a modified Serre–Green–Naghdi system
Oscillatory and regularized shock waves for a modified Serre–Green–Naghdi system Open
The Serre–Green–Naghdi equations of water wave theory have been widely employed to study undular bores. In this study, we introduce a modified Serre–Green–Naghdi system incorporating the effect of an artificial term that results in dispers…
View article: Oscillatory and regularized shock waves for a modified Serre-Green-Naghdi system
Oscillatory and regularized shock waves for a modified Serre-Green-Naghdi system Open
The Serre-Green-Naghdi equations of water wave theory have been widely employed to study undular bores. In this study, we introduce a modified Serre-Green-Naghdi system incorporating the effect of an artificial term that results in dispers…
View article: Axisymmetric flows with swirl for Euler and Navier-Stokes equations
Axisymmetric flows with swirl for Euler and Navier-Stokes equations Open
We consider the incompressible axisymmetric Navier-Stokes equations with swirl as an idealized model for tornado-like flows. Assuming an infinite vortex line which interacts with a boundary surface resembles the tornado core, we look for s…
View article: Renormalized solutions for the Maxwell--Stefan system with an application to uniqueness of weak solutions
Renormalized solutions for the Maxwell--Stefan system with an application to uniqueness of weak solutions Open
We give conditions that guarantee uniqueness of renormalized solutions for the Maxwell-Stefan system. The proof is based on an identity for the evolution of the symmetrized relative entropy. Using the method of doubling the variables we de…
View article: Alignment via friction for nonisothermal multicomponent fluid systems
Alignment via friction for nonisothermal multicomponent fluid systems Open
The derivation of an approximate Class-I model for nonisothermal multicomponent systems of fluids, as the high-friction limit of a Class-II model is justified, by validating the Chapman-Enskog expansion performed from the Class-II model to…
View article: Oscillatory and regularized shock waves for a dissipative Peregrine–Boussinesq system
Oscillatory and regularized shock waves for a dissipative Peregrine–Boussinesq system Open
We consider a dissipative, dispersive system of the Boussinesq type, which describes wave phenomena in scenarios where dissipation plays a significant role. Examples include undular bores in rivers or oceans, where turbulence-induced dissi…
View article: Existence and weak–strong uniqueness for Maxwell–Stefan–Cahn–Hilliard systems
Existence and weak–strong uniqueness for Maxwell–Stefan–Cahn–Hilliard systems Open
A Maxwell–Stefan system for fluid mixtures with driving forces depending on Cahn–Hilliard-type chemical potentials is analyzed. The corresponding parabolic cross-diffusion equations contain fourth-order derivatives and are considered in a …
View article: Existence and uniqueness for a viscoelastic Kelvin–Voigt model with nonconvex stored energy
Existence and uniqueness for a viscoelastic Kelvin–Voigt model with nonconvex stored energy Open
We consider nonlinear viscoelastic materials of Kelvin–Voigt-type with stored energies satisfying an Andrews–Ball condition, allowing for nonconvexity in a compact set. Existence of weak solutions with deformation gradients in [Formula: se…
View article: Zero-electron-mass and quasi-neutral limits for bipolar Euler-Poisson systems
Zero-electron-mass and quasi-neutral limits for bipolar Euler-Poisson systems Open
We consider a set of bipolar Euler-Poisson equations and study two asymptotic limiting processes. The first is the zero-electron-mass limit, which formally results in a non-linear adiabatic electron system. In a second step, we analyse the…
View article: Self-similar axisymmetric flows with swirl
Self-similar axisymmetric flows with swirl Open
We consider an infinite vortex line in a fluid which interacts with a boundary surface as a simplified model for tornadoes. We study self-similar solutions for stationary axisymmetric Navier-Stokes equations and investigate the types of mo…
View article: Non-isothermal multicomponent flows with mass diffusion and heat conduction
Non-isothermal multicomponent flows with mass diffusion and heat conduction Open
A type-I model of non-isothermal multicomponent systems of gases describing mass diffusive and heat conductive phenomena is presented. The derivation of the model and a convergence result among thermomechanical theories in the smooth regim…
View article: Dispersive shocks in diffusive-dispersive approximations of elasticity and quantum-hydrodynamics
Dispersive shocks in diffusive-dispersive approximations of elasticity and quantum-hydrodynamics Open
The aim is to assess the combined effect of diffusion and dispersion on shocks in the moderate dispersion regime. For a diffusive dispersive approximation of the equations of one-dimensional elasticity (or p-system), we study convergence o…
View article: Oscillatory and regularized shock waves for a dissipative Peregrine-Boussinesq system
Oscillatory and regularized shock waves for a dissipative Peregrine-Boussinesq system Open
We consider a dissipative, dispersive system of Boussinesq type, describing wave phenomena in settings where dissipation has an effect. Examples include undular bores in rivers or oceans where dissipation due to turbulence is important for…
View article: Asymptotic derivation of multicomponent compressible flows with heat conduction and mass diffusion
Asymptotic derivation of multicomponent compressible flows with heat conduction and mass diffusion Open
A Type-I model of a multicomponent system of fluids with non-constant temperature is derived as the high-friction limit of a Type-II model via a Chapman-Enskog expansion. The asymptotic model is shown to fit into the general theory of hype…
View article: Optimization Methods for One Dimensional Elastodynamics
Optimization Methods for One Dimensional Elastodynamics Open
We propose a new approach for solving systems of conservation laws that admit a variational formulation of the time-discretized form, and encompasses the p-system or the system of elastodynamics. The approach consists of using constrained …
View article: Weak-Strong Uniqueness for Maxwell--Stefan Systems
Weak-Strong Uniqueness for Maxwell--Stefan Systems Open
The weak-strong uniqueness for Maxwell--Stefan systems and some generalized systems is proved. The corresponding parabolic cross-diffusion equations are considered in a bounded domain with no-flux boundary conditions. The key points of the…
View article: Existence and weak-strong uniqueness for Maxwell-Stefan-Cahn-Hilliard systems
Existence and weak-strong uniqueness for Maxwell-Stefan-Cahn-Hilliard systems Open
A Maxwell-Stefan system for fluid mixtures with driving forces depending on Cahn-Hilliard-type chemical potentials is analyzed. The corresponding parabolic cross-diffusion equations contain fourth-order derivatives and are considered in a …
View article: Asymptotic derivation of multicomponent compressible flows with heat conduction and mass diffusion
Asymptotic derivation of multicomponent compressible flows with heat conduction and mass diffusion Open
A Type-I model of a multicomponent system of fluids with non-constant temperature is derived as the high-friction limit of a Type-II model via a Chapman-Enskog expansion. The asymptotic model is shown to fit into the general theory of hype…
View article: Weak-strong uniqueness for Maxwell-Stefan systems
Weak-strong uniqueness for Maxwell-Stefan systems Open
The weak-strong uniqueness for Maxwell--Stefan systems and some generalized systems is proved. The corresponding parabolic cross-diffusion equations are considered in a bounded domain with no-flux boundary conditions. The key points of the…
View article: The relaxation limit of bipolar fluid models
The relaxation limit of bipolar fluid models Open
This work establishes the relaxation limit from the bipolar Euler-Poisson system to the bipolar drift-diffusion system, for data so that the latter has a smooth solution. A relative energy identity is developed for the bipolar fluid models…
View article: An Energy Stable and Positivity-Preserving Scheme for the Maxwell--Stefan Diffusion System
An Energy Stable and Positivity-Preserving Scheme for the Maxwell--Stefan Diffusion System Open
We develop a new finite difference scheme for the Maxwell-Stefan diffusion system. The scheme is conservative, energy stable and positivity-preserving. These nice properties stem from a variational structure and are proved by reformulating…