Estimates for the nonlinear viscoelastic damped wave equation on compact Lie groups

Nonlinear damped wave equation arising in viscoelastic fluid flows

We consider the nonlinear damped wave equation arising in unsteady Poiseuille flow of shear thinning Maxwell fluid. We show the global existence of the smooth solution to the corresponding nonlinear system. We also give some numerical examples. c © 2006 Elsevier Ltd. All rights reserved.

Probability on Compact Lie Groups

Schauder Estimates on Lie Groups

Wave equation and multiplier estimates on ax + b groups

Let L be the distinguished Laplacian on certain semidirect products of R by R which are of ax+ b type. We prove pointwise estimates for the convolution kernels of spectrally localized wave operators of the form e √ ψ( √ L/λ) for arbitrary time t and arbitrary λ > 0, where ψ is a smooth bump function supported in [−2, 2] if λ ≤ 1 and in [1, 2] if λ ≥ 1. As a corollary, we reprove a basic multipl...

Compact Lie Groups

The first half of the paper presents the basic definitions and results necessary for investigating Lie groups. The primary examples come from the matrix groups. The second half deals with representation theory of groups, particularly compact groups. The end result is the Peter-Weyl theorem.