In this paper we prove the logarithmically improved Beale-Kato-Majda's criterion to the three-dimensional incompressible Euler and Navier-Stokes equations as well as the logarithmically improved Serrin's criteria to the three-dimensional incompressible Navier-Stokes equations.

The biorthogonality condition for Stokes flow in annular trenches bounded by horizontal parallel planes and concentric vertical cylinders is derived. This condition, is needed to compute the coefficients of the eigenfunction expansion solution of the corresponding Stokes flow problem.

Zakharov-Shabat–Ablowitz-Kaup-Newel-Segur (ZS–AKNS) representation for Stokes-anti-Stokes stimulated Raman scattering (SRS) is proposed. Periodical waves, solitons and self-similarity solutions are derived. Transient and bright threshold solitons are discussed. December 29, 1994 Sofia

In this paper we prove a global well-posedness result for tridimensional Navier-Stokes-Boussinesq system with axisymmetric initial data. This system couples Navier-Stokes equations with a transport equation governing the density.

The Stokes–Einstein relation has long been regarded as one of the hallmarks of transport in liquids. It predicts that the self-diffusion constant D is proportional to (τ/T)−1, where τ is the structural relaxation time and T is the temperature. Here, we present experimental data on water confirming that, below a crossover temperature T× ≈ 290 K, the Stokes– Einstein relation is replaced by a ‘fr...

-In order to calculate the mean mass flux past a given recording station it is necessary to know more than the mean velocity in a fixed, vertical section. One must add an additional term--the ' Stokes velocity ' which depends also oil the time and distance scales of the fluctuating currents. In typical circumstances, where the fluctuations are larger than the mean current, the Stokes velocity m...

We demonstrate coherent Raman spectroscopy (CRS) using a tunable excitation source based on a single femtosecond fiber laser. The frequency difference between the pump and the Stokes pulses was generated by soliton self-frequency shifting in a nonlinear optical fiber. Spectra of C─H stretches of cyclohexane were measured simultaneously by stimulated Raman gain (SRG) and coherent anti-Stokes Ram...

Cheyne-Stokes respiration is a form of periodic breathing in which central apneas and hypopneas alternate with periods of hyperventilation, producing a waxing and waning pattern of tidal volume. This review focuses on the causes and consequences of Cheyne-Stokes respiration in patients with congestive heart failure, in whom the prevalence is strikingly high and ranges from 30% to 50%. Several f...