@article{Socolowsky1994, author = {Socolowsky, J{\"u}rgen}, title = {Existence and uniqueness of the solution to a free boundary-value problem with thermocapillary convection in an unbounded domain}, series = {In: Acta Applicandae Mathematica November 37 (1994)1-2, pp 181-194}, journal = {In: Acta Applicandae Mathematica November 37 (1994)1-2, pp 181-194}, issn = {0167-8019 (print)}, doi = {10.1007/BF00995140}, pages = {181 -- 194}, year = {1994}, abstract = {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.}, language = {en} } @inproceedings{Socolowsky1995, author = {Socolowsky, J{\"u}rgen}, title = {Numerical analysis of viscous flows with free boundaries}, series = {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}, booktitle = {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}, pages = {1071 -- 1076}, year = {1995}, language = {en} } @inproceedings{Socolowsky1995, author = {Socolowsky, J{\"u}rgen}, title = {Analysis of a nonisothermal viscous flow problem with free boundaries and a dynamic contact line}, series = {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}, booktitle = {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}, pages = {201 -- 210}, year = {1995}, language = {en} } @article{Socolowsky1998, author = {Socolowsky, J{\"u}rgen}, title = {On the numerical solution of heat-conducting multiple-layer coating flows}, series = {In: Lithuanian Mathematical Journal 38 (1998) 1, pp 98-115}, journal = {In: Lithuanian Mathematical Journal 38 (1998) 1, pp 98-115}, issn = {0363-1672 (print)}, doi = {10.1007/BF02465548}, pages = {98 -- 116}, year = {1998}, language = {en} } @inproceedings{PileckasSocolowsky1998, author = {Pileckas, K. and Socolowsky, J{\"u}rgen}, title = {Analysis of the Navier-Stokes equations for some two-layer flows in unbounded domains}, series = {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}, booktitle = {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}, pages = {195 -- 216}, year = {1998}, language = {en} } @inproceedings{Socolowsky1998, author = {Socolowsky, J{\"u}rgen}, title = {Numerical studies of a nonisothermal two-layer curtain coating flow}, series = {In: Fluid mechanics of coating processes : proceedings / Euromech 367; Second European Coating Symposium (ECS '97), 22 - 25 July 1997, Universit{\´e} Louis Pasteur, Strasbourg, France. Ed.: Patrick Bourgin. - Strasbourg, 1997. - ISBN 2-909932-56-7}, booktitle = {In: Fluid mechanics of coating processes : proceedings / Euromech 367; Second European Coating Symposium (ECS '97), 22 - 25 July 1997, Universit{\´e} Louis Pasteur, Strasbourg, France. Ed.: Patrick Bourgin. - Strasbourg, 1997. - ISBN 2-909932-56-7}, pages = {339 -- 349}, year = {1998}, language = {en} } @inproceedings{Socolowsky1998, author = {Socolowsky, J{\"u}rgen}, title = {Analysis of free boundary value problems for some two-layer coating flows}, series = {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.}, booktitle = {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.}, pages = {13}, year = {1998}, language = {en} } @article{PileckasSocolowsky2002, author = {Pileckas, Konstantinas and Socolowsky, J{\"u}rgen}, title = {Analysis of Two Linearized Problems Modeling Viscous Two-Layer Flows}, series = {In: Mathematische Nachrichten 245 (2002) 1, 129-166}, journal = {In: Mathematische Nachrichten 245 (2002) 1, 129-166}, issn = {1522-2616}, doi = {10.1002/1522-2616(200211)245:1<129::AID-MANA129>3.0.CO;2-N}, pages = {129 -- 166}, year = {2002}, abstract = {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.}, language = {en} } @article{Socolowsky2004, author = {Socolowsky, J{\"u}rgen}, title = {On the existence and uniqueness of two-fluid channel flows}, series = {In: Mathematical modelling and analysis : the Baltic journal on mathematical applications, numerical analysis and differential equations 9 (2004) 1, 67-78}, journal = {In: Mathematical modelling and analysis : the Baltic journal on mathematical applications, numerical analysis and differential equations 9 (2004) 1, 67-78}, issn = {1392-6292}, pages = {67 -- 78}, year = {2004}, language = {en} } @article{PileckasSocolowsky2005, author = {Pileckas, K. and Socolowsky, J{\"u}rgen}, title = {Viscous two-fluid flows in perturbed unbounded domains}, series = {In: Mathematische Nachrichten 278 (2005) 5, 589-623,}, journal = {In: Mathematische Nachrichten 278 (2005) 5, 589-623,}, issn = {1522-2616 (online)}, doi = {10.1002/mana.200310260}, pages = {589 -- 623}, year = {2005}, abstract = {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)}, language = {en} }