Asymptotic analysis of magnetic induction with high frequency for solid conductors
The paper investigates the asymptotic behavior of a steady flow of an incompressible viscous fluid in a two-dimensional infinite pipe with slip boundary conditions and large flux. The convergence of the solutions to data at infinities is examined. The technique enables computing optimal factors of exponential decay at the outlet and inlet of the pipe which are unsymmetric for nonzero fluxes of the flow. As a corollary, the asymptotic structure of the solutions is obtained. The results show strong...
We construct global solutions to the Navier-Stokes equations with initial data small in a Besov space. Under additional assumptions, we show that they behave asymptotically like self-similar solutions.
Asymptotics of solutions to Schrödinger equations with singular magnetic and electric potentials is investigated. By using a Almgren type monotonicity formula, separation of variables, and an iterative Brezis–Kato type procedure, we describe the exact behavior near the singularity of solutions to linear and semilinear (critical and subcritical) elliptic equations with an inverse square electric potential and a singular magnetic potential with a homogeneity of order −1.
This paper deals with the evolution Fokker-Planck-Smoluchowski configurational probability diffusion equation for the FENE dumbbell model in dilute polymer solutions. We prove the exponential convergence in time of the solution of this equation to a corresponding steady-state solution, for arbitrary velocity gradients.
We study the one-dimensional motion of the viscous gas represented by the system , , with the initial and the boundary conditions , . We are concerned with the external forces, namely the function , which do not become small for large time . The main purpose is to show how the solution to this problem behaves around the stationary one, and the proof is based on an elementary -energy method.
The asymptotic behaviour of solutions of a class of free-boundary problems arising in vortex theory is discussed.