To the Jubilee of Vsevolod Alekseevich Solonnikov

Bibliography: 42 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 306, 2003, pp. 7–15.     

On Smoothness of Suitable Weak Solutions to the Navier-Stokes Equations

We prove two sufficient conditions for local regularity of suitable weak solutions to the three-dimensional Navier-Stokes equations. One of these conditions implies the smoothness of L_3,∞-solutions as a particular case. Bibliography: 12 titles.Dedicated to Vsevolod Alekseevich Solonnikov__________Published in Zapiski Nauchnykh Seminarov POMI, Vol. 306, 2003, pp. 186–198.     

Differential properties of solutions of evolution variational inequalities in the theory of plasticity

We study the differential properties of weak solutions of evolution variational inequalities in the theory of flow of elastoplastic media with hardening. We consider the two most popular models of hardening—isotropic and kinematic. The differential properties studied depend on the nature of the hardening. In the case of isotropic hardening great smoothness of the distributed load is required, and in this situation the result is the same for the stress tensor—it belongs to the class L (0,T;W _2,loc ¹ ).Bibliography: 10 titles. Translated fromProblemy Matematicheskogo Analiza, No. 12, 1992, pp. 153–173.     

Study of thermo-optical distortions in a plate active element with zigzag beam path

Phase distortions introduced into the laser beam propagating in a plate under diode pumping of the active element (AE) and for intentionally caused temperature gradients in the AE are studied. The temperature distribution along the optical axis of the active element is measured during its end diode pumping. Phase distortions of the test beam propagating through the nonuniformly heated active element are studied. Interference patterns are obtained and optical distortions of the test beam are measured at various temperature gradients in the crystal.     

Spectral-Luminescent Properties of Yb3+ in SOCl2–GaCl3

Optics and Spectroscopy - The absorption and luminescence spectra and the excited state lifetime of Yb3+ in SOCl2–GaCl3–Yb3+ solutions are measured. Information on the Stark splitting...     

Laser vibrometry based on analysis of the speckle pattern from a remote object

A novel technique is represented that allows one to measure vibrations from a distant object with micron and sub-micron amplitudes in real time.     

Extension of the variational formulation of the problem for a rigid-plastic medium to velocity fields with slip-type discontinuities

Sets of velocity fields containing slip-type discontinuities at the boundary of the rigid-plastic medium, as well as within it, and the functionals defined on these sets, are described. It is shown that the exact lower bounds of the variational problems for these functionals are equal to the coefficient of the critical load. The minimax problem with saddle point constructed here is regarded as an extension of the classical minimax problem of the theory of critical loads.