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

Piero D'Ancona; Damiano Foschi; Sigmund Selberg

Journal of the European Mathematical Society (2007)

- Volume: 009, Issue: 4, page 877-899
- ISSN: 1435-9855

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topD'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 -

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