51 research outputs found
L1 MAXIMAL REGULARITY FOR THE LAPLACIAN AND APPLICATIONS
Inter alia we prove L1 maximal regularity for the Laplacian in the space of Fourier transformed finite Radon measures FM. This is remarkable, since FM is not a UMD space and by the fact that we obtain Lp maximal regularity for p = 1, which is not even true for the Laplacian in L2. We apply our result in order to construct strong solutions to the Navier-Stokes equations for initial data in FM in a rotating frame. In particular, the obtained results are uniform in the angular velocity of rotation
-theory for a fluid-structure interaction model
We consider a fluid-structure interaction model for an incompressible fluid
where the elastic response of the free boundary is given by a damped Kirchhoff
plate model. Utilizing the Newton polygon approach, we first prove maximal
regularity in -Sobolev spaces for a linearized version. Based on this, we
show existence and uniqueness of the strong solution of the nonlinear system
for small data.Comment: 18 page
Stability Analysis for a Class of Heterogeneous Catalysis Models
We prove stability for a class of heterogeneous catalysis models in the
-setting. We consider a setting in a finite three-dimensional pore of
cylinder-like geometry, with the lateral walls acting as a catalytic surface.
Under a reasonable condition on the involved parameters, we show that given
equilibria are normally stable, i.e. solutions are attracted at an exponential
rate. The potential incidence of instability is discussed as well.Comment: 14 page
Global solvabiliy of the Navier-Stokes equations in spaces based on sum-closed frequency sets
We prove existence of global regular solutions for the 3D Navier-Stokes quations with (or without) Coriolis force for a class of initial data u0 in he space FM¾;± , i.e. for functions whose Fourier image bu0 is a vector-valued adon measure and that are supported in sum-closed frequency sets with istance ± from the origin. In our main result we establish an upper bound or admissible initial data in terms of the Reynolds number, uniform on the oriolis parameter . In particular this means that this upper bound is inearly growing in ±. This implies that we obtain global in time regular olutions for large (in norm) initial data u0 which may not decay at space nfinity, provided that the distance ± of the sum-closed frequency set from he origin is sufficiently large
Global Strong Solutions for a Class of Heterogeneous Catalysis Models
We consider a mathematical model for heterogeneous catalysis in a finite
three-dimensional pore of cylinder-like geometry, with the lateral walls acting
as a catalytic surface. The system under consideration consists of a
diffusion-advection system inside the bulk phase and a
reaction-diffusion-sorption system modeling the processes on the catalytic wall
and the exchange between bulk and surface. We assume Fickian diffusion with
constant coefficients, sorption kinetics with linear growth bound and a network
of chemical reactions which possesses a certain triangular structure. Our main
result gives sufficient conditions for the existence of a unique global strong
-solution to this model, thereby extending by now classical results on
reaction-diffusion systems to the more complicated case of heterogeneous
catalysis.Comment: 30 page
Tuning static drop friction
The friction force opposing the onset of motion of a drop on a solid surface is typically considered to be a material property for a fixed drop volume on a given surface. However, here we show that even for a fixed drop volume, the static friction force can be tuned by over 30% by preshaping the drop. The static friction usually exceeds the kinetic friction that the drop experiences when moving in a steady state. Both forces converge when the drop is prestretched in the direction of motion or when the drop shows low contact angle hysteresis. In contrast to static friction, kinetic friction is independent of preshaping the drop, that is, the drop history. Kinetic friction forces reflect the material properties
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