40 citations · 108 across the 12 of their papers we have counts for
16 papers
On the rigidity of rank gradient in a group of intermediate growth
Rostislav Grigorchuk, Rostyslav Kravchenko
We introduce and investigate the rigidity property of rank gradient in the case of the group of intermediate growth constructed by the first author. We show that $\mat…
Generators of maximal orders
Rostyslav V. Kravchenko, Marcin Mazur, Bogdan V. Petrenko
Let R be the ring of algebraic integers in a number field K and let L be a maximal order in a semisimple K-algebra B. Building on our previous work, we compute the smallest number…
Constructions of torsion-free countable, amenable, weakly mixing groups
Rostislav Grigorchuk, Rostyslav Kravchenko, Alexander Olshanskii
In this note, we construct torsion-free countable, amenable, weakly mixing groups, which answer a question of V. Bergelson. Some results related to verbal subgroups and crystallogr…
Characteristic random subgroups of geometric groups and free abelian groups of infinite rank
Lewis Bowen, Rostislav Grigorchuk, Rostyslav Kravchenko
We show that if is a non-elementary word hyperbolic group, mapping class group of a hyperbolic surface or the outer automorphism group of a nonabelian free group then has $…
A unified approach to determining forms for the 2D Navier-Stokes equations - the general interpolants case
Ciprian Foias, Michael S. Jolly, Rostyslav Kravchenko +1
In this paper we show that the long time dynamics (the global attractor) of the 2D Navier-Stokes equation is embedded in the long time dynamics of an ordinary differential equation…
Navier-Stokes equations, determining forms, determining modes, inertial manifolds, dissipative dynamical systems
Ciprian Foias, Michael S. Jolly, Rostyslav Kravchenko +1
The determining modes for the two-dimensional incompressible Navier-Stokes equations (NSE) are shown to satisfy an ordinary differential equation of the form , in the B…