Existence, uniqueness, and quasilinearization results for nonlinear differential equations arising in viscoelastic fluid flow.
For a bounded domain , we use the notion of very weak solutions to obtain a new and large uniqueness class for solutions of the inhomogeneous Navier-Stokes system , , with , , and very general data classes for , , such that may have no differentiability property. For smooth data we get a large class of unique and regular solutions extending well known classical solution classes, and generalizing regularity results. Moreover, our results are closely related to those of a series of...
We consider the spatially inhomogeneous Bekker-Döring infinite-dimensional kinetic system describing the evolution of coagulating and fragmenting particles under the influence of convection and diffusion. The simultaneous consideration of opposite coagulating and fragmenting processes causes many additional difficulties in the investigation of spatially inhomogeneous problems, where the space variable changes differently for distinct particle sizes. To overcome these difficulties, we use a modified...
We study eigenfrequencies and propagator expansions for damped wave equations on compact manifolds. In the strongly damped case, the propagator is shown to admit an expansion in terms of the finitely many eigenmodes near the real axis, with an error exponentially decaying in time. In the presence of an elliptic closed geodesic not meeting the support of the damping coefficient, we show that there exists a sequence of eigenfrequencies converging rapidly to the real axis. In the case of Zoll manifolds,...