DCDS-S
New developments in mathematical theory of fluid mechanics
Eduard Feireisl Šárka Nečasová Reimund Rautmann Werner Varnhorn
Discrete & Continuous Dynamical Systems - S 2014, 7(5): i-ii doi: 10.3934/dcdss.2014.7.5i
Mathematical theory of fluid mechanics is a field with a rich long history and active present. The volume collects selected contributions of distinguished experts in various domains ranging from modeling through mathematical analysis to numerics and practical implementations related to real world problems.

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DCDS-S
Lower and upper bounds to the change of vorticity by transition from slip- to no-slip fluid flow
Reimund Rautmann
Discrete & Continuous Dynamical Systems - S 2014, 7(5): 1101-1109 doi: 10.3934/dcdss.2014.7.1101
For the transition from slip- to no-slip fluid flow, we establish lower and upper bounds to the resulting change of the $L^2$-norm of the vorticity. Moreover we present a transport-diffusion splitting scheme, built up solely by a transport step and subsequent diffusion step (without any additional vorticity creation operator as introduced in former studies by Lighthill, Marsden, and Chorin), the splitting scheme being consistent with the Navier-Stokes equations with no-slip condition.
keywords: Transition from slip- to no-slip flow orthogonal decomposition of $W^{1 change of vorticity transport-diffusion splitting schemes. 2}$
DCDS-S
Preface
Šárka Nečasová Reimund Rautmann Werner Varnhorn
Discrete & Continuous Dynamical Systems - S 2010, 3(2): i-ii doi: 10.3934/dcdss.2010.3.2i
This Volume of Discrete and Continuous Dynamical Systems is dedicated to Professor Vsevolod Aleksevich Solonnikov on the occasion of his 75th birthday.
   He was born on June 8th, 1933 in Leningrad. Working at the Department of the Steklov Mathematical Institute in today St. Petersburg for more than 50 years he has published nearly 250 scientific papers on the theory of partial differential equations and function theory. Moreover, he was teaching for 20 years at the Chair of Mathematical Physics at the Faculty of Mathematics and Mechanics at Leningrad State University. He has many pupils. Under his supervision, two doctoral and eight candidate theses were defended. He regularly participates in international scientific conferences all over the world. He is speaking at least six European languages.

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