251 research outputs found
Kernel estimates for nonautonomous Kolmogorov equations with potential term
Using time dependent Lyapunov functions, we prove pointwise upper bounds for
the heat kernels of some nonautonomous Kolmogorov operators with possibly
unbounded drift and diffusion coefficients and a possibly unbounded potential
term
Compactness and asymptotic behavior in nonautonomous linear parabolic equations with unbounded coefficients in
We consider a class of second order linear nonautonomous parabolic equations
in R^d with time periodic unbounded coefficients. We give sufficient conditions
for the evolution operator G(t,s) be compact in C_b(R^d) for t>s, and describe
the asymptotic behavior of G(t,s)f as t-s goes to infinity in terms of a family
of measures mu_s, s in R, solution of the associated Fokker-Planck equation
L\sp p-estimates for a class of elliptic operators with unbounded coefficients in \bold R\sp N
On the Navier-Stokes equations with rotating effect and prescribed outflow velocity
We consider the equations of Navier-Stokes modeling viscous fluid flow past a
moving or rotating obstacle in subject to a prescribed velocity
condition at infinity. In contrast to previously known results, where the
prescribed velocity vector is assumed to be parallel to the axis of rotation,
in this paper we are interested in a general outflow velocity. In order to use
-techniques we introduce a new coordinate system, in which we obtain a
non-autonomous partial differential equation with an unbounded drift term. We
prove that the linearized problem in is solved by an evolution
system on for . For this we use
results about time-dependent Ornstein-Uhlenbeck operators. Finally, we prove,
for and initial data , the
existence of a unique mild solution to the full Navier-Stokes system.Comment: 18 pages, to appear in J. Math. Fluid Mech. (published online first
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