53 citations · 290 across the 46 of their papers we have counts for
51 papers
Finite-energy weak solutions and relaxation for a compressible kinetic--fluid system with locally averaged Brinkman force
Young-Pil Choi, Roman Shvydkoy
We study a kinetic--fluid system in which a Vlasov or Vlasov--Fokker--Planck equation is coupled to the compressible Navier--Stokes equations with density-dependent viscosities thr…
On the inviscid instability of the 2D Taylor-Green vortex
Xinyu Zhao, Bartosz Protas, Roman Shvydkoy
We consider Euler flows on two-dimensional (2D) periodic domain and are interested in the stability, both linear and nonlinear, of a simple equilibrium given by the 2D Taylor-Green…
Continuous model of opinion dynamics with convictions
Vinh Nguyen, Roman Shvydkoy
In this note we study a new kinetic model of opinion dynamics. The model incorporates two forces -- alignment of opinions under all-to-all communication driving the system to a con…
Environmental Averaging
Roman Shvydkoy
Many classical examples of models of self-organized dynamics, including the Cucker-Smale, Motsch-Tadmor, multi-species, and several others, include an alignment force that is based…
Volumetric theory of intermittency in fully developed turbulence
Alexey Cheskidov, Roman Shvydkoy
This study introduces a new family of volumetric flatness factors which give a rigorous parametric description of the phenomenon of intermittency in fully developed turbulent flows…
Propagation of Chaos for the Cucker-Smale Systems under heavy tail communication
Vinh Nguyen, Roman Shvydkoy
In this work we study propagation of chaos for solutions of the Liouville equation for the classical discrete Cucker-Smale system. Assuming that the communication kernel satisfies…