Null structure and almost optimal local regularity for the Dirac-Klein-Gordon system

D'Ancona, Piero, Foschi, Damiano, and Selberg, Sigmund. "Null structure and almost optimal local regularity for the Dirac-Klein-Gordon system." Journal of the European Mathematical Society 009.4 (2007): 877-899. <http://eudml.org/doc/277678>.

@article{DAncona2007,
abstract = {We prove almost optimal local well-posedness for the coupled Dirac–Klein–Gordon (DKG) system of equations in $1+3$ dimensions. The proof relies on the null structure of the system, combined with bilinear spacetime estimates of Klainerman–Machedon type. It has been known for some time that the Klein–Gordon part of the system has a null structure; here we uncover an additional null structure in the Dirac equation, which cannot be seen directly, but appears after a duality argument.},
author = {D'Ancona, Piero, Foschi, Damiano, Selberg, Sigmund},
journal = {Journal of the European Mathematical Society},
keywords = {Dirac equation; Klein-Gordon equation; null structure; local well-posedness; null form estimates; Dirac equation; Klein-Gordon equation; null structure; local well-posedness; null form estimates},
language = {eng},
number = {4},
pages = {877-899},
publisher = {European Mathematical Society Publishing House},
title = {Null structure and almost optimal local regularity for the Dirac-Klein-Gordon system},
url = {http://eudml.org/doc/277678},
volume = {009},
year = {2007},
}

TY - JOUR
AU - D'Ancona, Piero
AU - Foschi, Damiano
AU - Selberg, Sigmund
TI - Null structure and almost optimal local regularity for the Dirac-Klein-Gordon system
JO - Journal of the European Mathematical Society
PY - 2007
PB - European Mathematical Society Publishing House
VL - 009
IS - 4
SP - 877
EP - 899
AB - We prove almost optimal local well-posedness for the coupled Dirac–Klein–Gordon (DKG) system of equations in $1+3$ dimensions. The proof relies on the null structure of the system, combined with bilinear spacetime estimates of Klainerman–Machedon type. It has been known for some time that the Klein–Gordon part of the system has a null structure; here we uncover an additional null structure in the Dirac equation, which cannot be seen directly, but appears after a duality argument.
LA - eng
KW - Dirac equation; Klein-Gordon equation; null structure; local well-posedness; null form estimates; Dirac equation; Klein-Gordon equation; null structure; local well-posedness; null form estimates
UR - http://eudml.org/doc/277678
ER -