91 citations · 382 across the 40 of their papers we have counts for
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Derivation of effective kinetic equations describing oscillations in viscoelasticity and in compressible Navier-Stokes
Athanasios E. Tzavaras
These lecture notes are devoted to solutions of hyperbolic-parabolic systems with persistent oscillations. We consider two examples both from mechanics: (i) The system of viscoelas…
Local analytic well-posedness for one-dimensional Vlasov$\unicode{x2013}$Dirac$\unicode{x2013}$Benney-type equations
Nuno J. Alves, Peter Markowich, Athanasios E. Tzavaras
We study a one-dimensional nonlinear Vlasov equation with a local self-consistent force field generated by the density, where the force is given by the spatial derivative of a real…
Asymptotic Limits for Strain-Gradient Viscoelasticity with Nonconvex Energy
Aseel AlNajjar, Stefano Spirito, Athanasios E. Tzavaras
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\rig…
A bilinear fractional integral operator for Euler-Riesz systems
Nuno J. Alves, Loukas Grafakos, Athanasios E. Tzavaras
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…
Strong convergence of sequences with vanishing relative entropy
Nuno J. Alves, Jakub Skrzeczkowski, Athanasios E. Tzavaras
We show that under natural growth conditions on the entropy function, convergence in relative entropy is equivalent to -convergence. The main tool is the theory of Young measu…
Sustained Oscillations in Hyperbolic-Parabolic Systems
Athanasios E. Tzavaras
We construct examples of oscillating solutions with persistent oscillations for various hyperbolic-parabolic systems with singular diffusion matrices that appear in mechanics. Thes…
Oscillations in Compressible Navier-Stokes and Homogenization in Phase Transition problems
Athanasios E. Tzavaras
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…
Zero-electron-mass and quasi-neutral limits for bipolar Euler-Poisson systems
Nuno J. Alves, Athanasios E. Tzavaras
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…
Non-isothermal multicomponent flows with mass diffusion and heat conduction
Stefanos Georgiadis, Ansgar Jüngel, Athanasios Tzavaras
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…
Self-similar axisymmetric flows with swirl
Theodoros Katsaounis, Ioanna Mousikou, Athanasios E. Tzavaras
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 axisymmet…
Dispersive shocks in diffusive-dispersive approximations of elasticity and quantum-hydrodynamics
Daria Bolbot, Dimitrios Mitsotakis, Athanasios E. Tzavaras
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-d…
Oscillatory and regularized shock waves for a dissipative Peregrine-Boussinesq system
Larkspur Brudvik-Lindner, Dimitrios Mitsotakis, Athanasios E. Tzavaras
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…
Existence and weak-strong uniqueness for Maxwell-Stefan-Cahn-Hilliard systems
Xiaokai Huo, Ansgar Jüngel, Athanasios E. Tzavaras
A Maxwell-Stefan system for fluid mixtures with driving forces depending on Cahn-Hilliard-type chemical potentials is analyzed. The corresponding parabolic cross-diffusion equation…
Asymptotic derivation of multicomponent compressible flows with heat conduction and mass diffusion
Stefanos Georgiadis, Athanasios E. Tzavaras
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 asymp…
Weak-strong uniqueness for Maxwell-Stefan systems
Xiaokai Huo, Ansgar Jüngel, Athanasios E. Tzavaras
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 dom…
Existence and uniqueness for a viscoelastic Kelvin-Voigt model with nonconvex stored energy
Konstantinos Koumatos, Corrado Lattanzio, Stefano Spirito +1
We consider nonlinear viscoelastic materials of Kelvin-Voigt type with stored energies satisfying an Andrews-Ball condition, allowing for non convexity in a compact set. Existence…
The relaxation limit of bipolar fluid models
Nuno J. Alves, Athanasios E. Tzavaras
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 relativ…
A discrete variational scheme for isentropic processes in polyconvex thermoelasticity
Cleopatra Christoforou, Myrto Galanopoulou, Athanasios E. Tzavaras
We propose a variational scheme for the construction of isentropic processes of the equations of adiabatic thermoelasticity with polyconvex internal energy. The scheme hinges on th…
High-friction limits of Euler flows for multicomponent systems
Xiaokai Huo, Ansgar Jüngel, Athanasios E. Tzavaras
The high-friction limit in Euler-Korteweg equations for fluid mixtures is analyzed. The convergence of the solutions towards the zeroth-order limiting system and the first-order co…
Measure-valued solutions for the equations of polyconvex adiabatic thermoelasticity
Cleopatra Christoforou, Myrto Galanopoulou, Athanasios E. Tzavaras
For the system of polyconvex adiabatic thermoelasticity, we define a notion of dissipative measure-valued solution, which can be considered as the limit of a viscosity approximatio…
Conservation of energy for the Euler-Korteweg equations
Tomasz Dębiec, Piotr Gwiazda, Agnieszka Świerczewska-Gwiazda +1
In this article we study the principle of energy conservation for the Euler-Korteweg system. We formulate an Onsager-type sufficient regularity condition for weak solutions of the…
A symmetrizable extension of polyconvex thermoelasticity and applications to zero-viscosity limits and weak-strong uniqueness
Cleopatra Christoforou, Myrto Galanopoulou, Athanasios E. Tzavaras
We embed the equations of polyconvex thermoviscoelasticity into an augmented, symmetrizable, hyperbolic system and derive a relative entropy identity in the extended variables. Fol…
Localization in adiabatic shear flow via geometric theory of singular perturbations
Min-Gi Lee, Theodoros Katsaounis, Athanasios Tzavaras
We study localization occurring during high speed shear deformations of metals leading to the formation of shear bands. The localization instability results from the competition am…
Stability properties of the Euler-Korteweg system with nonmonotone pressures
Jan Giesselmann, Athanasios E. Tzavaras
We establish a relative energy framework for the Euler-Korteweg system with non-convex energy. This allows us to prove weak-strong uniqueness and to show convergence to a Cahn-Hill…