This series of books forms a unique and rigorous treatise on various mathematical aspects
of fluid mechanics models. These models consist of systems of nonlinear partial differential …

We study the incompressible Navier Stokes equations in Rn_R+ ut+(u}{) u&2u+{p= 0 {{} u=
0(1) u (0)= u0, where u is the velocity and p is the pressure. It is well known that the Navier …

Fluid dynamics is an ancient science incredibly alive today. Modern technol ogy and new
needs require a deeper knowledge of the behavior of real fluids, and new discoveries or …

We also consider the Cauchy problem for the Navier-Stokes equation on Rn for n> 2 of the
following form: where u= u (t, x) is an Rn-valued function standing for the velocity at (t, x) …

1. Introduction We are interested in the nonstationary threedimensional flow of a viscous
incompressible fluid when the initial vorticity is very singular. The governing equations of …

Data from ab-oriented YBa 2 Cu 3 O 7/I/Cu tunnel junctions are presented. Self-assembled
monolayers form the insulating tunnel barrier, I. The YBa 2 Cu 3 O 7 features in the tunneling …

In the study of the initial value problem for the Navier-Stokes equations, du-+ V, u= vLu-grad
p, div u= 0, u (0)= f,(1.1) at there is considerable interest in demonstrating the existence of a …

We consider the nonlinear Schrödinger equation (NLS)(see below) with a general
“potential” F (u), for which there are in general no conservation laws. The main assumption …

It is shown that the nonstationary Navier-Stokes equation (NS) in ℝ+× ℝ m is well posed in
certain Morrey spaces M p, λ (ℝ+× ℝ m)(see the text for the definition: in particular M p, 0= L …

This paper is devoted to the analysis of function spaces modeled on Besov spaces and their
applications to non-linear partial differential equations, with emphasis on the …