For linear Volterra difference equations, some stability properties of the zero solution are studied in connection with the summability of the fundamental solution. Also, for perturbed equations with asymptotically almost periodic forcing term, the existence of asymptotically almost periodic solutions is shown under some condition on stabilities.
This paper is concerned with the stationary Navier-Stokes equations in exterior domains of dimension n≥3, and provides a sufficient condition on the external force for the unique solvability. This condition is valid both in the case with small but nonzero velocity at infinity, and in the case with zero velocity at infinity. As a result it is proved that, if the external force satisfies this condition, the solution with nonzero velocity at infinity converges to the solution with zero velocity at infinity with respect to the weak-* topology of appropriate function spaces.
Let G be a real rank one connected semisimple Lie group with finite center. We introduce a real Hardy space H1 (G//K) on G as the space consisting of all K-bi-invariant functions f on G whose radial maximal functions Mφf are integrable on G. We shall obtain a relation between H1 (G//K) and H1(R), the real Hardy space on the real line R, via the Abel transform on G and give a characterization of H1 (G//K).
In this paper, we define some invariants of polynomial functions which are derivative from invariants of polarized varieties, and we study their properties. As applications, by using their invariants, we study polarized toric varieties, and we also classify finite partially ordered sets.
We prove global existence of solutions to multiple speed, Dirichlet-wave equations with quadratic nonlinearities satisfying the null condition in the exterior of compact obstacles. This extends the result of our previous paper by allowing general higher order terms. In the currect setting, these terms are much more difficult to handle than for the free wave equation, and we do so using an analog of a pointwise estimate due to Kubota and Yokoyama.