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Existence, uniqueness and regularity of stationary solutions to inhomogeneous Navier-Stokes equations in n

Reinhard Farwig, Hermann Sohr (2009)

Czechoslovak Mathematical Journal

For a bounded domain Ω n , n 3 , we use the notion of very weak solutions to obtain a new and large uniqueness class for solutions of the inhomogeneous Navier-Stokes system - Δ u + u · u + p = f , div u = k , u | Ω = g with u L q , q n , and very general data classes for f , k , g such that u 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...

Existence, uniqueness and stability for spatially inhomogeneous Becker-Döring equations with diffusion and convection terms

P. B. Dubovski, S.-Y. Ha (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

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...

Expansions and eigenfrequencies for damped wave equations

Michael Hitrik (2001)

Journées équations aux dérivées partielles

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,...

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