zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Global strong solution to the Thirring model in critical space. (English) Zbl 1218.81077
Summary: We obtain a strong solution in charge critical space L 2 () of the Thirring system and Federbusch equations in one space dimension by using solution representation of the models. The uniqueness is obtained for the solution ΨL ([0,T];L 2 ()L 4 ()). A decay of local charge and asymptotic behavior of the field can be shown directly.
MSC:
81T10Model quantum field theories
81U15Exactly and quasi-solvable systems (quantum theory)
81Q80Special quantum systems, such as solvable systems
References:
[1]Thirring, W. E.: A soluble relativistic field theory, Ann. phys. 3, 91-112 (1958) · Zbl 0078.44303 · doi:10.1016/0003-4916(58)90015-0
[2]Delgado, V.: Global solutions of the Cauchy problem for the (classical) coupled Maxwell-Dirac and other nonlinear Dirac equations in one space dimension, Proc. amer. Math. soc. 69, No. 2, 289-296 (1978) · Zbl 0351.35003 · doi:10.2307/2042613
[3]Salusti, E.; Tesei, A.: On a semi-group approach to quantum field equations, Nuovo cimento A 11, 122-138 (1971)
[4]Dias, J. -P.; Figueira, M.: Time decay for the solutions of a nonlinear Dirac equation, Ric. mat. 35, 308-316 (1981) · Zbl 0658.35076
[5]Selberg, S.; Tesfahun, A.: Low regularity well-posedness for some nonlinear Dirac equations in one space dimension, Differential integral equations 23, No. 3-4, 265-278 (2010)
[6]Bournaveas, N.: Local and global solutions for a nonlinear Dirac system, Adv. differential equations 9, No. 5-6, 677-698 (2004) · Zbl 1103.35087
[7]Bournaveas, N.: Local well-posedness for a nonlinear Dirac equation in spaces of almost critical dimension, Discrete contin. Dyn. syst. 20, No. 3, 605-616 (2008) · Zbl 1144.35306 · doi:10.3934/dcds.2008.20.605
[8]Escobedo, M.; Vega, L.: A semilinear Dirac equation in Hs(R3) for s>1, SIAM J. Math. anal. 28, No. 2, 338-362 (1997)
[9]Machihara, S.; Omoso, T.: The explicit solutions to the nonlinear Dirac equation and Dirac-Klein-Gordon equation, Ric. mat. 56, No. 1, 19-30 (2007) · Zbl 1146.35021 · doi:10.1007/s11587-007-0002-9
[10]Zhou, Y.: Uniqueness of weak solutions in 1+1 dimensional wave maps, Math. Z. 232, 707-719 (1999) · Zbl 0940.35141 · doi:10.1007/PL00004779