6 papers
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…
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…
Variational structure of Fokker-Planck equations with variable mobility
Hailiang Liu, Athanasios E. Tzavaras
We study Fokker--Planck equations with symmetric, positive definite mobility matrices capturing diffusion in heterogeneous environments. A weighted Wasserstein metric is introduced…
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\ri…
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…