75 citations · 323 across the 24 of their papers we have counts for
25 papers
Depletion of nonlinearity in space-analytic space-periodic solutions to equations of diffusive magnetohydrodynamics
Vladislav Zheligovsky
We consider solenoidal space-periodic space-analytic solutions to the equations of magnetohydrodynamics. An elementary bound shows that due to the special structure of the nonlinea…
Space analyticity and bounds for derivatives of solutions to the evolutionary equations of diffusive magnetohydrodynamics
Vladislav Zheligovsky
In 1981, Foias, Guillopé and Temam proved a priori estimates for arbitrary-order space derivatives of solutions to the Navier-Stokes equation. Such bounds are instructive in the nu…
Computation of kinematic and magnetic -effect and eddy diffusivity tensors by Padé approximation
Sílvio M. A. Gama, Roman Chertovskih, Vladislav Zheligovsky
We present examples of Padé approximation of the -effect and eddy viscosity/diffusivity tensors in various flows. Expressions for the tensors derived in the framework of the sta…
Pointwise vanishing velocity helicity of a flow does not preclude magnetic field generation
Alexander Andrievsky, Roman Chertovskih, Vladislav Zheligovsky
Pointwise zero velocity helicity density is shown not to prevent steady flows from acting as kinematic dynamos. We present numerical evidences that such flows can generate both sma…
Negative magnetic eddy diffusivity due to oscillogenic -effect
Alexander Andrievsky, Roman Chertovskih, Vladislav Zheligovsky
We study large-scale kinematic dynamo action of steady mirror-antisymmetric flows of incompressible fluid, that involve small spatial scales only, by asymptotic methods of the mult…
Magnetic field generation by pointwise zero-helicity three-dimensional steady flow of incompressible electrically conducting fluid
A. Rasskazov, R. Chertovskih, V. Zheligovsky
We introduce six families of three-dimensional space-periodic steady solenoidal flows, whose kinetic helicity density is zero at any point. Four families are analytically defined.…