Wojciech M. Zaja̧czkowski

WAY 100135, an Antagonist of 5-HT1A Serotonin Receptors, Attenuates Psychotomimetic Effects of MK-801

In the present study, we investigated whether the antagonist of 5-HT1A receptors, WAY 100135, was capable of modifying the psychostimulant and psychotomimetic effects of MK-801, a non-competitive antagonist of NMDA receptors. It was found that: 1) WAY 100135 (10 and 20 mg/kg, but not 1.25, 2.5, and 5 mg/kg) transiently, in a dose dependent manner, attenuated the locomotor stimulant effects of MK-801 (0.4 mg/kg). Given alone, WAY 100135 had no effect on the locomotor activity of rats; 2) WAY 100135 (1.25 and 2.5 mg/kg, but not 10 or 20 mg/kg), attenuated or abolished the disruptive effects of MK-801 on the sensorimotor gating measured in a prepulse-induced inhibition of the acoustic startle response paradigm. WAY 100135 in all tested doses had no effect on the sensorimotor gating or amplitude of the acoustic startle response; 3) WAY 100135 (1.25, 2.5 mg/kg, but not 5 mg/kg) attenuated the detrimental effects of MK-801 on working memory and selective attention, measured in a delayed alternation task. Again, given alone, WAY 100135 did not influence the behavior of rats in that experimental paradigm; and 4) MK-801 (0.4 mg/kg) had no effect on the 5-HT1A receptor mRNA level in rat hippocampus, measured 2 and 24 hours after MK-801 administration. These data indicate that 5-HT1A receptors might be involved in the psychotomimetic effects of non-competitive NMDA receptor antagonists. In addition, 5-HT1A serotonin receptor antagonists and partial agonists may have potential antipsychotic properties.

Global Regular Solutions to a Kelvin--Voigt Type Thermoviscoelastic System

A classical three-dimensional thermoviscoelastic system of Kelvin--Voigt type is considered. The existence and uniqueness of a global regular solution is proved without small data assumption. The existence proof is based on the successive approximation method. The crucial part constitutes a priori estimates on an arbitrary finite time interval, which are derived with the help of the theory of anisotropic Sobolev spaces with a mixed norm.

Quantitative robustness of regularity for 3D Navier–Stokes system in Ḣα-spaces

Abstract We present stability and regularity results for the 3D incompressible Navier–Stokes system in a periodic box, in H α spaces, with α ∈ [ 1 / 2 , 1 ] . A special attention is paid to obtaining quantitative results, i.e. ones with explicit or at least computable constants, and to scaling.

Local and Global Solutions Near Equilibria via the Energy Method

In this chapter we present the classical energy approach for existence of regular solutions to the equations of compressible, heat-conducting fluids in a bounded three-dimensional domain. Firstly, we provide a state of the art and recall representative results in this field. Next, we give a proof of one of them, concerning Dirichlet boundary conditions for velocity and temperature. The result and thus the proof is divided into two main parts. A local-in-time existence result in high-regularity norms, via a method of successive approximations, occupies the former one. In the latter part, a differential inequality is derived, which allows us to extend the local-in-time solution to the global-in-time solution, provided a certain smallness condition is satisfied. This smallness condition is in fact an equilibrium proximity condition, since it involves differences between data and constants, whereas the data for temperature and density may be large themselves. All our considerations are performed within the L2-approach. The proved result is close to that of Valli and Zaja̧czkowski (Commun Math Phys 103:259–296, 1986), but the techniques used here: the method of successive approximations (instead of a Leray-Schauder fixed-point argument there) as well as a clear continuation argument renders our exposition more traceable. Moreover, one J. Burczak ( ) Institute of Mathematics, Polish Academy of Sciences, Warsaw, Poland OxPDE, Mathematical Institute, University of Oxford, Oxford, UK e-mail: jb@impan.pl Y. Shibata Department of Mathematics and Research Institute of Science and Engineering, Waseda University, Shinjuku-ku, Tokyo, Japan e-mail: yshibata@waseda.jp W.M. Zaja̧czkowski Institute of Mathematics, Polish Academy of Sciences, Warsaw, Poland Institute of Mathematics and Cryptology, Cybernetics Faculty, Military University of Technology, Warsaw, Poland e-mail: wz@impan.pl

Global Nonstationary Navier--Stokes Motion with Large Flux

We show the existence of global in time regular solutions for the nonstationary inflow-outflow problem in a cylindrical pipe. The motion of the fluid is modeled using the Navier--Stokes system with the slip boundary conditions. Some balance estimates on external forces and the derivatives of the inflow function are imposed but the flux is arbitrarily large. Those assumptions and smallness of the parameter reciprocal to the existence time

Global existence to a three‐dimensional non‐linear thermoelasticity system arising in shape memory materials

T

Stability of two-dimensional Navier–Stokes motions in the periodic case

permit us to continue the local solutions to the global ones.