Tomáš Bárta

Moving contact line of a volatile fluid

Interfacial flows close to a moving contact line are inherently multiscale. The shape of the interface and the flow at meso- and macroscopic scales inherit an apparent interface slope and a regularization length, both named after Voinov, from the microscopic inner region. Here, we solve the inner problem associated with the contact line motion for a volatile fluid at equilibrium with its vapor. The evaporation or condensation flux is then controlled by the dependence of the saturation temperature on interface curvature-the so-called Kelvin effect. We derive the dependencies of the Voinov angle and of the Voinov length as functions of the parameters of the problem. We then identify the conditions under which the Kelvin effect is indeed the mechanism regularizing the contact line motion.

SMOOTH SOLUTIONS OF VOLTERRA EQUATIONS VIA SEMIGROUPS

In this paper we introduce a class of left shift semigroups that are differentiable. With the help of perturbation theory for differentiable semigroups we show that solutions of an integrodifferential equation can be infinitely differentiable if the convolution kernel is sufficiently smooth and regular. 1991 Mathematics subject classification: primary 47D06; secondary 45D05.

MOAT FLOW SYSTEM AROUND SUNSPOTS IN SHALLOW SUBSURFACE LAYERS

We investigate the subsurface moat flow system around McIntosh H-type symmetrical sunspots and compare it to the flow system within supergranular cells. Representatives of both types of flows are constructed by means of the statistical averaging of flow maps obtained by time-distance helioseismic inversions. We find that moat flows around H-type sunspots replace supergranular flows but there are two principal differences between the two phenomena: the moat flow is asymmetrical, probably due to the proper motion of sunspots with respect to the local frame of rest, while the flow in the supergranular cell is highly symmetrical. Furthermore, the whole moat is a downflow region, while the supergranule contains the upflow in the center, which turns into the downflow at about 60% of the cell radius from its center. We estimate that the mass downflow rate in the moat region is at least two times larger than the mass circulation rate within the supergranular cell.

ON R-SECTORIAL DERIVATIVES ON BERGMAN SPACES

In this paper we show boundedness of vector-valued Bergman projections on simple connected domains. With this result we show R-sectoriality of the derivative on the Bergman space on C + and maximal L p -regularity for an integrodifferential equation with a kernel in the Bergman space.

Global existence for a system of nonlocal PDEs with applications to chemically reacting incompressible fluids

We show global existence for a class of models of fluids that change their properties depending on the concentration of a chemical. We allow that the stress tensor in (t, x) depends on the velocity and concentration at other points and times. The example we have in mind foremost are materials with memory.