This work is concerned with the large time behavior of solutions to barotropic compressible Navier-Stokes equations in R d ( ≥ 2 ) . A pure energy argument independent spectral analysis has been developed more general L p framework, which enables us not only obtain optimal time-decay rates but also remove smallness low frequencies initial data that required previous studies on this problem. The...

McNicol K N, et al. Spectrum of asthma in children. I. Clinical and physiological components; II. Allergic components; III. Psychological and social components. Br MedJ 1973; iv: 7-11; 12-6; 16-20. 2 Murray A B, Fraser B M, Hardwick D F, Pirie G E. Letter: Chronic asthma and growth failure in children. Lancet 1976; ii: 197-8. Kerrebijn K F, De Kroon J P M. Effect on height of corticosteroid the...

the ponseti method is a safe and effective treatment for congenital clubfoot, and radically decreases the need for extensive corrective surgery. but a group of patients will still present with under corrected residual equinovarus deformities despite the proper use of the ponseti method. about 25% of operated clubfeet will develop recurrence or show a marked residual deformity (recurrent clubfoo...

We prove the existence of global in time solution to Kolmogorov’s two-equation model turbulence three dimensional domain with periodic boundary conditions under smallness assumption imposed on initial data.

A finite element heterogeneous multiscale method is proposed for solving the Stokes problem in porous media. The method is based on the coupling of an effective Darcy equation on a macroscopic mesh, with unknown permeabilities recovered from micro finite element calculations for Stokes problems on sampling domains centered at quadrature points in each macro element. The numerical method account...

We study the solvability of second boundary value problem a class highly singular, fully nonlinear fourth order equations Abreu type in higher dimensions under either smallness condition or radial symmetry.