{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,28]],"date-time":"2025-03-28T10:17:37Z","timestamp":1743157057069,"version":"3.40.3"},"publisher-location":"Cham","reference-count":24,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030000479"},{"type":"electronic","value":"9783030000493"}],"license":[{"start":{"date-parts":[[2018,1,1]],"date-time":"2018-01-01T00:00:00Z","timestamp":1514764800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2018]]},"DOI":"10.1007\/978-3-030-00049-3_2","type":"book-chapter","created":{"date-parts":[[2018,9,7]],"date-time":"2018-09-07T08:32:37Z","timestamp":1536309157000},"page":"19-37","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Some Applications of Parabolic Dirac Operators to the Instationary Navier-Stokes Problem on Conformally Flat Cylinders and Tori in $$\\mathbb {R}^3$$"],"prefix":"10.1007","author":[{"given":"P.","family":"Cerejeiras","sequence":"first","affiliation":[]},{"given":"U.","family":"K\u00e4hler","sequence":"additional","affiliation":[]},{"given":"R. S.","family":"Krau\u00dfhar","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,9,8]]},"reference":[{"issue":"3","key":"2_CR1","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1080\/10652460108819346","volume":"12","author":"H Bahmann","year":"2001","unstructured":"Bahmann, H., G\u00fcrlebeck, K., Shapiro, M., Spr\u00f6\u00dfig, W.: On a modified teodorescu transform. Integral Transf. Spec. Funct. 12(3), 213\u2013226 (2001)","journal-title":"Integral Transf. Spec. Funct."},{"issue":"5","key":"2_CR2","doi-asserted-by":"publisher","first-page":"429","DOI":"10.1080\/17476930500481400","volume":"51","author":"S Bernstein","year":"2006","unstructured":"Bernstein, S.: Factorization of the nonlinear Schr\u00f6dinger equation and applications. Complex Var. Elliptic Equ. 51(5), 429\u2013452 (2006)","journal-title":"Complex Var. Elliptic Equ."},{"key":"2_CR3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1515\/crelle.2010.042","volume":"643","author":"E Bulla","year":"2010","unstructured":"Bulla, E., Constales, D., Krau\u00dfhar, R.S., Ryan, J.: Dirac type operators for arithmetic subgroups of generalized modular groups. Journal f\u00fcr die Reine und Angewandte Mathematik 643, 1\u201319 (2010)","journal-title":"Journal f\u00fcr die Reine und Angewandte Mathematik"},{"issue":"1","key":"2_CR4","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1002\/(SICI)1099-1476(20000110)23:1<81::AID-MMA105>3.0.CO;2-Z","volume":"23","author":"P Cerejeiras","year":"2000","unstructured":"Cerejeiras, P., K\u00e4hler, U.: Elliptic boundary value problems of fluid dynamics over unbounded domains. Math. Methods Appl. Sci. 23(1), 81\u2013101 (2000)","journal-title":"Math. Methods Appl. Sci."},{"issue":"14","key":"2_CR5","doi-asserted-by":"publisher","first-page":"1715","DOI":"10.1002\/mma.634","volume":"28","author":"P Cerejeiras","year":"2005","unstructured":"Cerejeiras, P., K\u00e4hler, U., Sommen, F.: Parabolic Dirac operators and the Navier-Stokes equations over time-varying domains. Math. Methods Appl. Sci. 28(14), 1715\u20131724 (2005)","journal-title":"Math. Methods Appl. Sci."},{"issue":"4","key":"2_CR6","doi-asserted-by":"publisher","first-page":"535","DOI":"10.1002\/mma.1050","volume":"32","author":"P Cerejeiras","year":"2009","unstructured":"Cerejeiras, P., Vieira, N.: Regularization of the non-stationary Schr\u00f6dinger operator. Math. Methods Appl. Sci. 32(4), 535\u2013555 (2009)","journal-title":"Math. Methods Appl. Sci."},{"issue":"6","key":"2_CR7","doi-asserted-by":"publisher","first-page":"735","DOI":"10.1002\/mma.941","volume":"31","author":"D Constales","year":"2008","unstructured":"Constales, D., Krau\u00dfhar, R.S.: On the Navier-Stokes equation with Free Convection in three dimensional triangular channels. Math. Methods Appl. Sci. 31(6), 735\u2013751 (2008)","journal-title":"Math. Methods Appl. Sci."},{"issue":"16","key":"2_CR8","doi-asserted-by":"publisher","first-page":"2050","DOI":"10.1002\/mma.1122","volume":"32","author":"D Constales","year":"2009","unstructured":"Constales, D., Krau\u00dfhar, R.S.: Multiperiodic eigensolutions to the Dirac operator and applications to the generalized Helmholtz equation on flat cylinders and on the $$n$$-torus. Math. Methods Appl. Sci. 32(16), 2050\u20132070 (2009)","journal-title":"Math. Methods Appl. Sci."},{"issue":"4","key":"2_CR9","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1002\/mma.1224","volume":"33","author":"D Constales","year":"2010","unstructured":"Constales, D., Grob, D., Krau\u00dfhar, R.S.: On generalized Helmholtz type equations in concentric annular domains in $$\\mathbb{R}^3$$. Math. Meth. Appl. Sci. 33(4), 431\u2013438 (2010)","journal-title":"Math. Meth. Appl. Sci."},{"key":"2_CR10","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-2922-0","volume-title":"Clifford Algebra and Spinor Valued Functions","author":"R Delanghe","year":"1992","unstructured":"Delanghe, R., Sommen, S., Sou\u010dek, V.: Clifford Algebra and Spinor Valued Functions. Kluwer, Dortrecht, Boston, London (1992)"},{"issue":"6","key":"2_CR11","doi-asserted-by":"publisher","first-page":"577","DOI":"10.1080\/10236190600637965","volume":"12","author":"N Faustino","year":"2006","unstructured":"Faustino, N., G\u00fcrlebeck, K., Hommel, A., K\u00e4hler, U.: Difference potentials for the Navier-Stokes equations in unbounded domains. J. Differ. Equ. Appl. 12(6), 577\u2013595 (2006)","journal-title":"J. Differ. Equ. Appl."},{"key":"2_CR12","series-title":"Applications to mathematics, Physics, and Engineering, Progress in Mathematical Physics","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1007\/978-1-4612-2044-2_3","volume-title":"Clifford algebras","author":"K G\u00fcrlebeck","year":"2004","unstructured":"G\u00fcrlebeck, K., Hommel, A.: On discrete Stokes and Navier-Stokes equations in the plane. In: Ablamowicz, R. (ed.) Clifford algebras. Applications to mathematics, Physics, and Engineering, Progress in Mathematical Physics, vol. 34, pp. 35\u201358. Birkh\u00e4user, Boston (2004)"},{"key":"2_CR13","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-7295-9","volume-title":"Quaternionic Analysis and Elliptic Boundary Value Problems","author":"K G\u00fcrlebeck","year":"1990","unstructured":"G\u00fcrlebeck, K., Spr\u00f6\u00dfig, S.: Quaternionic Analysis and Elliptic Boundary Value Problems. Birkh\u00e4user, Basel (1990)"},{"key":"2_CR14","volume-title":"Quaternionic and Clifford Calculus for Physicists and Engineers","author":"K G\u00fcrlebeck","year":"1997","unstructured":"G\u00fcrlebeck, K., Spr\u00f6\u00dfig, S.: Quaternionic and Clifford Calculus for Physicists and Engineers. Wiley, Chichester, New York (1997)"},{"issue":"1","key":"2_CR15","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1016\/j.jmaa.2006.01.045","volume":"325","author":"RS Krau\u00dfhar","year":"2007","unstructured":"Krau\u00dfhar, R.S., Ryan, J.: Some conformally flat spin manifolds, dirac operators and automorphic forms. J. Math. Anal. Appl. 325(1), 359\u2013376 (2007)","journal-title":"J. Math. Anal. Appl."},{"key":"2_CR16","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1007\/s00028-010-0089-4","volume":"11","author":"RS Krau\u00dfhar","year":"2011","unstructured":"Krau\u00dfhar, R.S., Vieira, N.: The Schr\u00f6dinger equation on cylinders and the $$n$$-torus. J. Evol. Equ. 11, 215\u2013237 (2011)","journal-title":"J. Evol. Equ."},{"key":"2_CR17","volume-title":"Applied Quaternionic Analysis, Research and Exposition in Mathematics","author":"V Kravchenko","year":"2003","unstructured":"Kravchenko, V.: Applied Quaternionic Analysis, Research and Exposition in Mathematics, vol. 28. Heldermann Verlag, Lemgo (2003)"},{"key":"2_CR18","volume-title":"Integral Representations for Spatial Models of Mathematical Physics","author":"V Kravchenko","year":"1996","unstructured":"Kravchenko, V., Shapiro, M.: Integral Representations for Spatial Models of Mathematical Physics. Addison Wesley Longman, Harlow (1996)"},{"key":"2_CR19","doi-asserted-by":"publisher","first-page":"916","DOI":"10.2307\/1969587","volume":"50","author":"NH Kuiper","year":"1949","unstructured":"Kuiper, N.H.: On conformally flat spaces in the large. Ann. Math. 50, 916\u2013924 (1949)","journal-title":"Ann. Math."},{"key":"2_CR20","volume-title":"Spin Geometry","author":"HB Lawson","year":"1989","unstructured":"Lawson, H.B., Michelsohn, M.-L.: Spin Geometry. Princeton University Press, New York (1989)"},{"key":"2_CR21","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0073556","volume-title":"Clifford Wavelets, Singular Integrals and Hardy Spaces","author":"M Mitrea","year":"1994","unstructured":"Mitrea, M.: Clifford Wavelets, Singular Integrals and Hardy Spaces. Lecture Notes in Mathematics. Springer, New York (1994)"},{"key":"2_CR22","doi-asserted-by":"publisher","first-page":"1355","DOI":"10.1002\/mma.375","volume":"25","author":"M Mitrea","year":"2002","unstructured":"Mitrea, M.: Boundary value problems for Dirac operators and Maxwell\u2019s equations in non-smooth domains. Math. Math. Appl. Sci. 25, 1355\u20131369 (2002)","journal-title":"Math. Math. Appl. Sci."},{"key":"2_CR23","unstructured":"Spr\u00f6\u00dfig, W.: Forecasting equations in complex quaternionic setting. In: Simos, T.E. (ed.), Recent Advances in Computational and Applied Mathematics, European Academy of Science. Springer, Doordrecht (Chapter 12)"},{"key":"2_CR24","doi-asserted-by":"publisher","first-page":"445","DOI":"10.1090\/S0894-0347-99-00290-8","volume":"12","author":"S Wu","year":"1999","unstructured":"Wu, S.: Well-posedness in Sobolev spaces of the full water wave problem in 3D. J. Am. Math. Soc. 12, 445\u2013495 (1999)","journal-title":"J. Am. Math. Soc."}],"container-title":["Springer Proceedings in Mathematics &amp; Statistics","Clifford Analysis and Related Topics"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-00049-3_2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,10]],"date-time":"2024-07-10T01:53:20Z","timestamp":1720576400000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-030-00049-3_2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018]]},"ISBN":["9783030000479","9783030000493"],"references-count":24,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-00049-3_2","relation":{},"ISSN":["2194-1009","2194-1017"],"issn-type":[{"type":"print","value":"2194-1009"},{"type":"electronic","value":"2194-1017"}],"subject":[],"published":{"date-parts":[[2018]]},"assertion":[{"value":"CART","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Clifford Analysis and Related Topics","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Tallahassee, FL","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"USA","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2014","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"15 December 2014","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"17 December 2014","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"cart2014","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/www.math.fsu.edu\/cart2014\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}