TY - JOUR A1 - Socolowsky, Jürgen T1 - Existence and uniqueness of the solution to a free boundary-value problem with thermocapillary convection in an unbounded domain JF - In: Acta Applicandae Mathematica November 37 (1994)1-2, pp 181-194 N2 - A free boundary-value problem for a nonisothermal flow of two heavy viscous incompressible capillary liquids descibing a slot coating process is mathematically studied. The problem is stationary and two-dimensional and the Boussinesq approximation for the Navier-Stokes equations is used. The existence and uniqueness of a weak solution is proved in weighted Holder spaces for small data. Y1 - 1994 U6 - https://doi.org/10.1007/BF00995140 SN - 0167-8019 (print) SN - 1572-9036 (online) SP - 181 EP - 194 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 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 - Socolowsky, Jürgen T1 - On various types of viscous two-fluid flows JF - In: Banach Center publications 81 (2008), 481-491 N2 - Viscous two-fluid flows arise in different kinds of coating technologies. Frequently, the corresponding mathematical models represent two-dimensional free boundary value problems for the Navier-Stokes equations or their modifications. In this review article we present some results about nonisothermal stationary as well as about isothermal evolutionary viscous flow problems. The temperature-depending problems are characterized by coupled heat- and mass transfer and also by thermocapillary convection. The solvability of two related problems is discussed. Also, an evolutionary problem on the viscous (isothermal) flow of two connected fluids down an inclined plane is investigated. Y1 - 2008 U6 - https://doi.org/10.4064/bc81-0-30 SN - 0137-6934 (print) SN - 1730-6299 (online) SP - 481 EP - 491 ER - TY - JOUR A1 - Socolowsky, Jürgen T1 - The evolution of a viscpus two-fluid flow down an inclined plane JF - In: Proceedings in applied mathematics and mechanics : PAMM 7 (2007) 1, 2100033–2100034 N2 - An evolutionary problem on the viscous (isothermal) flow of two connected fluids down an inclined plane is investigated. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) Y1 - 2007 U6 - https://doi.org/10.1002/pamm.200700244 SN - 1617-7061 SP - 2100033 EP - 2100034 ER - TY - JOUR A1 - Socolowsky, Jürgen T1 - On the Nusselt solution of a nonisothermal two-fluid inclined film flow JF - In: International journal of mathematics and mathematical sciences : IJMMS (2009), Article ID 981983, 8 pages N2 - Nonisothermal viscous two-fluid flows occur in numerous kinds of coating devices. The corresponding mathematical models often represent two-dimensional free boundary value problems for the Navier-Stokes equations or their modifications. In the present paper we are concerned with a particular problem of coupled heat and mass transfer. Marangoni convection is incorporated, too. The solvability of a corresponding stationary problem is discussed. The obtained results generalize previous results for a similar isothermal problem. Y1 - 2009 U6 - https://doi.org/10.1155/2009/981983 SN - 1687-0425 (online) SN - 0161-1712 (print) ER - TY - JOUR A1 - Socolowsky, Jürgen T1 - On a two-fluid inclined film flow with evaporation JF - In: Mathematical modelling and analysis : the Baltic journal on mathematical applications, numerical analysis and differential equations 18 (2013) 1, 22-31 Y1 - 2013 SN - 1392-6292 SP - 22 EP - 31 ER - TY - JOUR A1 - Socolowsky, Jürgen T1 - The solvability of a two-layer slot coating flow with evaporation JF - Journal of Coupled Systems and Multiscale Dynamics 1(2013) 4, 434-441 Y1 - 2013 U6 - https://doi.org/10.1166/jcsmd.2013.1033 SN - 2330-152X (print) SN - 2330-1538 (online) SP - 434 EP - 441 ER - TY - JOUR A1 - Socolowsky, Jürgen T1 - The solvability of a free boundary problem for the stationary Navier-Stokes equations with a dynamic contact line JF - In: Nonlinear Analysis: Theory, Methods & Applications 21 (1993) 10, 763–784 Y1 - 1993 SP - 763 EP - 784 ER - TY - JOUR A1 - Socolowsky, Jürgen A1 - Wolff, M. T1 - On some model problems in flow problems with contact angles JF - In: Zeitschrift für angewandte Mathematik und Mechanik : ZAMM = Journal of applied mathematics and mechanics 74 (1994) 11, 557-558 Y1 - 1994 U6 - https://doi.org/10.1002/zamm.19940741113 SP - 557 EP - 558 ER - TY - CHAP A1 - Socolowsky, Jürgen T1 - The analysis of a coating flow with evaporation T2 - In: Analysis and approximation of boundary value problems : a memorial meeting dedicated to prof. Valery Rivkind / edited by Pekka Neittaanmäki, Ludmila Rivkind. - yväskylä : University of Jyväskylä, 2000. - (Reports of the Department of Mathematical Information Technology / University of Jyväskylä. Series A, Collections, ISSN 1456-4351; 2/2000). - ISBN 951-39-0689-2 Y1 - 2000 SP - 209 EP - 225 ER - TY - INPR A1 - Socolowsky, Jürgen T1 - The analysis of a coating flow with evaporation T2 - In: IMA Preprint Series Aug. 1998, No. 1587, 1-20 Y1 - 1998 UR - http://www.ima.umn.edu/preprints/AUG98/1587.pdf ER - TY - CHAP A1 - Socolowsky, Jürgen T1 - Study of two perturbed two-layer coating flows T2 - In: 10th International Coating Science and Technology Syposium : final program and extended abstracts. - Minnesota : Univ., 2000 Y1 - 2000 SP - 36 EP - 39 ER - TY - GEN A1 - Socolowsky, Jürgen T1 - On a two-layer slot coating flow with evaporation Y1 - 2013 ER - TY - JOUR A1 - Socolowsky, Jürgen T1 - On a viscous two-fluid channel flow including evaporation JF - Open Mathematics Y1 - 2018 U6 - https://doi.org/10.1515/math-2018-0001 SN - 2391-5455 (Online) VL - 16 IS - 1 SP - 9 EP - 15 PB - De Gruyter ER -