Well-posedness for nonlinear Dirac equations in one dimension
Machihara, Shuji ; Nakanishi, Kenji ; Tsugawa, Kotaro
Kyoto J. Math., Tome 50 (2010) no. 2, p. 403-451 / Harvested from Project Euclid
We completely determine the range of Sobolev regularity for the Dirac- Klein-Gordon system, the quadratic nonlinear Dirac equations, and the wave-map equation to be well posed locally in time on the real line. For the Dirac-Klein-Gordon system, we can continue those local solutions in nonnegative Sobolev spaces by the charge conservation. In particular, we obtain global well-posedness in the space where both the spinor and scalar fields are only in $L^2({\mathbb R})$ . Outside the range for well-posedness, we show either that some solutions exit the Sobolev space instantly or that the solution map is not twice differentiable at zero.
Publié le : 2010-05-15
Classification:  35L70,  35L71,  35B44,  35B65,  35Q41
@article{1273236821,
     author = {Machihara, Shuji and Nakanishi, Kenji and Tsugawa, Kotaro},
     title = {Well-posedness for nonlinear Dirac equations in one dimension},
     journal = {Kyoto J. Math.},
     volume = {50},
     number = {2},
     year = {2010},
     pages = { 403-451},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1273236821}
}
Machihara, Shuji; Nakanishi, Kenji; Tsugawa, Kotaro. Well-posedness for nonlinear Dirac equations in one dimension. Kyoto J. Math., Tome 50 (2010) no. 2, pp.  403-451. http://gdmltest.u-ga.fr/item/1273236821/