TY - JOUR A1 - Socolowsky, Jürgen T1 - On nonisothermal two‐fluid channel flows JF - In: Mathematical modelling and analysis : the Baltic journal on mathematical applications, numerical analysis and differential equations 12 (2007) 1, 143-156 N2 - Two‐fluid channel flows arise in different kinds of coating technologies. The corresponding mathematical models represent two‐dimensional free boundary value problems for the Navier‐Stokes equations or their modifications. In this paper we are concerned with the so‐called Boussinesq‐approximation of the coupled heat‐ and mass transfer. Thermocapillary convection is included. The solvability of two related stationary problems is discussed. The solution techniques of both problems are quite different. The obtained results generalize previous results for similar isothermal problems. Y1 - 2007 U6 - https://doi.org/10.3846/1392-6292.2007.12.143-156 SN - 1392-6292 (print) SN - 1648-3510 (online) SP - 143 EP - 156 ER - TY - JOUR A1 - Pileckas, K. A1 - Socolowsky, Jürgen T1 - Viscous two-fluid flows in perturbed unbounded domains JF - In: Mathematische Nachrichten 278 (2005) 5, 589–623, N2 - Two stationary plane free boundary value problems for the Navier-Stokes equations are studied. The first problem models the viscous two-fluid flow down a perturbed or slightly distorted inclined plane. The second one describes the viscous two-fluid flow in a perturbed or slightly distorted channel. For sufficiently small data and under certain conditions on parameters the solvability and uniqueness results are proved for both problems. The asymptotic behaviour of the solutions is investigated. For the second problem an example of nonuniqueness is constructed. Computational results of flow problems that are very close to the above problems are presented. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) Y1 - 2005 U6 - https://doi.org/10.1002/mana.200310260 SN - 1522-2616 (online) SN - 0025-584X (print) SP - 589 EP - 623 ER - TY - JOUR A1 - Socolowsky, Jürgen T1 - On the existence and uniqueness of two-fluid channel flows JF - In: Mathematical modelling and analysis : the Baltic journal on mathematical applications, numerical analysis and differential equations 9 (2004) 1, 67-78 Y1 - 2004 SN - 1392-6292 SP - 67 EP - 78 ER - TY - GEN A1 - Brasche, Ulrich T1 - Debt-overhang and ways out N2 - The focus of this paper is legacy debt and ways out of it. It introduces credit, debt and financial stress as a basis for understanding the ongoing financial crisis as well as solutions discussed in politics and media. We clarify why and when debt is too much, and discuss ways of avoiding outright default. The main questions are • What are the basics of debt and related financial problems? • How much debt is too much? • Why and when is default a problem to all of us? • Is there a way out of the current debt crisis? While debt and looming bankruptcy of governments is the focus of media attention, we will not neglect the fact, that households, banks and companies in many countries acquired too much debt as well and are therefore a source of problems of their own right. KW - legacy debt KW - bankruptcy KW - haircut KW - euro crisis KW - financial crisis Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:522-opus4-9204 SP - 1 EP - 65 ER - TY - JOUR A1 - Pileckas, Konstantinas A1 - Socolowsky, Jürgen T1 - Analysis of Two Linearized Problems Modeling Viscous Two-Layer Flows JF - In: Mathematische Nachrichten 245 (2002) 1, 129–166 N2 - Two problems that appear in the linearization of certain free boundary value problems of the hydrodynamics of two viscous fluids are studied in the strip-like domain Π = {x = (x1, x2) ∈ ℝ2 : x1 ∈ ℝ1, (0 < x2 < h*) ∨ (h* < x2 < 1)}. The first problem arises in the linearization of a two-layer flow down a geometrically perturbed inclined plane. The second one appears after the linearization of a two-layer flow in a geometrically perturbed inclined channel with one moving (smooth) wall. For this purpose the unknown flow domain was mapped onto the double strip Π. The arising linear elliptic problems contain additional unknown functions in the boundary conditions. The paper is devoted to the investigation of these boundary problems by studying the asymptotics of the eigenvalues of corresponding operator pencils. It can be proved that the boundary value problems are uniquely solvable in weighted Sobolev spaces with exponential weight. The study of the full (nonlinear) free boundary value problems will be the topic of a forthcoming paper. Y1 - 2002 U6 - https://doi.org/10.1002/1522-2616(200211)245:1<129::AID-MANA129>3.0.CO;2-N SN - 1522-2616 SN - 0025-584X (print) SP - 129 EP - 166 ER - TY - CHAP A1 - Socolowsky, Jürgen T1 - Analysis of free boundary value problems for some two-layer coating flows T2 - In: Final program and extended abstracts / 9th International Coating Science and Technology Symposium : May 17 - 20, 1998, University of Delaware, Newark, Delaware / sponsored by ISCST, International Society of Coating Science and Technology. - Newark, Del., 1998. - XXVI, 386 S. Y1 - 1998 ER - TY - CHAP A1 - Socolowsky, Jürgen T1 - Numerical studies of a nonisothermal two-layer curtain coating flow T2 - In: Fluid mechanics of coating processes : proceedings / Euromech 367; Second European Coating Symposium (ECS '97), 22 - 25 July 1997, Université Louis Pasteur, Strasbourg, France. Ed.: Patrick Bourgin. - Strasbourg, 1997. - ISBN 2-909932-56-7 Y1 - 1998 SP - 339 EP - 349 ER - TY - CHAP A1 - Pileckas, K. A1 - Socolowsky, Jürgen T1 - Analysis of the Navier-Stokes equations for some two-layer flows in unbounded domains T2 - In: Navier stokes equations and related nonlinear problems : proceedings of the Sixth International Conference NSEC-6, Palanga, Lithuania, May 22 - 29, 1997 / ed.: H. Amann ... Utrecht [u.a.] : VSP [u.a.], 1998. - ISBN 90-6764-288-6 Y1 - 1998 SP - 195 EP - 216 ER - TY - JOUR A1 - Socolowsky, Jürgen T1 - On the numerical solution of heat-conducting multiple-layer coating flows JF - In: Lithuanian Mathematical Journal 38 (1998) 1, pp 98-115 Y1 - 1998 U6 - https://doi.org/10.1007/BF02465548 SN - 0363-1672 (print) SN - 1573-8825 (online) SP - 98 EP - 116 ER - TY - CHAP A1 - Socolowsky, Jürgen T1 - Analysis of a nonisothermal viscous flow problem with free boundaries and a dynamic contact line T2 - In: Navier-Stokes equations and related nonlinear problems : [proceedings of the Third International Conference on Navier-Stokes Equations and Related Nonlinear Problems, held May 21 - 27, 1994, in Funchal, Madeira, Portugal] / ed. by A. Sequeira. - New York [u.a.] : Plenum Press, 1995. - ISBN: 0-306-45118-2 Y1 - 1995 SP - 201 EP - 210 ER - TY - CHAP A1 - Socolowsky, Jürgen T1 - Numerical analysis of viscous flows with free boundaries T2 - In: Simulation of materials processing : theory, methods and applications ; proceedings of the Fifth International Conference on Numerical Methods in Industrial Forming Processes, NUMIFORM '95, Ithaca, New York, USA, 18 - 21 June 1995 / ed. by Shan-Fu Shen .... - Rotterdam [u.a.] : Balkema, 1995. - ISBN: 90-5410-553-4 Y1 - 1995 SP - 1071 EP - 1076 ER -