We prove that the Yang-Mills equation in Lorenz gauge in the (3+1)-dimensional case is locally well-posed for data of the gauge potential in $H^s$ and the curvature in $H^r$, where $s >\frac{5}{7}$ and $r > -\frac{1}{7}$, respectively. This improves a result by Tesfahun [
Citation: |
P. d'Ancona
, D. Foschi
and S. Selberg
, Atlas of products for wave-Sobolev spaces on $\mathbb{R}^{1+3}$, Trans. Amer. Math. Soc., 364 (2012)
, 31-63.
doi: 10.1090/S0002-9947-2011-05250-5.![]() ![]() ![]() |
|
P. d'Ancona
, D. Foschi
and S. Selberg
, Null structure and almost optimal local well-posedness of the Maxwell-Dirac system, Amer. J. Math., 132 (2010)
, 771-839.
doi: 10.1353/ajm.0.0118.![]() ![]() ![]() |
|
J. Ginibre
and G. Velo
, Generalized Strichartz inequalities for the wave equation, J. Funct. Anal., 133 (1995)
, 60-68.
doi: 10.1006/jfan.1995.1119.![]() ![]() ![]() |
|
S. Klainerman
and M. Machedon
, Finite energy solutions of the Yang-Mills equations in ${\mathbb R}^{3+1}$, Ann. of Math., 142 (1995)
, 39-119.
doi: 10.2307/2118611.![]() ![]() ![]() |
|
S. Klainerman and M. Machedon (Appendices by J. Bougain and D. Tataru), Remark on Strichartz-type inequalities, Int. Math. Res. Not. IMRN, 5 (1996), 201-220.
doi: 10.1155/S1073792896000153.![]() ![]() ![]() |
|
S. Klainerman
and S. Selberg
, Bilinear estimates and applications to nonlinear wave equations, Commun. Contemp. Math., 4 (2002)
, 223-295.
doi: 10.1142/S0219199702000634.![]() ![]() ![]() |
|
S. Klainerman
and D. Tataru
, On the optimal local regularity for the Yang-Mills equations in $\mathbb{R}^{4+1}$, J. Amer. Math. Soc., 12 (1999)
, 93-116.
doi: 10.1090/S0894-0347-99-00282-9.![]() ![]() ![]() |
|
J. Krieger and J. Sterbenz, Global regularity for the Yang-Mills equations on high dimensonal Minkowski space, Mem. Amer. Math. Soc., 223 (2013), No. 1047
doi: 10.1090/S0065-9266-2012-00566-1.![]() ![]() ![]() |
|
J. Krieger
and D. Tataru
, Global well-posedness for the Yang-Mills equations in 4+1 dimensions. Small energy, Ann. of Math., 185 (2017)
, 831-893.
doi: 10.4007/annals.2017.185.3.3.![]() ![]() ![]() |
|
S. Oh
, Gauge choice for the Yang-Mills equations using the Yang-Mills heat flow and local well-posedness in H1, J. Hyperbolic Differ. Equ., 11 (2014)
, 1-108.
doi: 10.1142/S0219891614500015.![]() ![]() ![]() |
|
S. Oh
, Finite energy global well-posedness of the Yang-Mills equations on $\mathbb{R}^{1+3}$ : an approach using the Yang-Mills heat flow, Duke Math. J., 164 (2015)
, 1669-1732.
doi: 10.1215/00127094-3119953.![]() ![]() ![]() |
|
H. Pecher
, Local well-posedness for the (n+1)-dimensional Yang-Mills and Yang-Mills-Higgs system in temporal gauge, NoDEA Nonlinear Differential Equations Appl., 23 (2016)
, 23-40.
doi: 10.1007/s00030-016-0395-9.![]() ![]() ![]() |
|
S. Selberg
and A. Tesfahun
, Finite-energy global well-posedness of the Maxwell-Klein-Gordon system in Lorenz gauge, Comm. Partial Differential Equations, 35 (2010)
, 10290-1057.
doi: 10.1080/03605301003717100.![]() ![]() ![]() |
|
S. Selberg
and A. Tesfahun
, Null structure and local well-posedness in the energy class for the Yang-Mills equations in Lorenz gauge, J. Eur. Math. Soc. (JEMS), 18 (2016)
, 1729-1752.
doi: 10.4171/JEMS/627.![]() ![]() ![]() |
|
T. Tao
, Local well-posedness of the Yang-Mills equation in the temporal gauge below the energy norm, J. Differential Equations, 189 (2003)
, 366-382.
doi: 10.1016/S0022-0396(02)00177-8.![]() ![]() ![]() |
|
A. Tesfahun
, Local well-posedness of Yang-Mills equations in Lorenz gauge below the energy norm, NoDEA Nonlinear Differential Equations Appl., 22 (2015)
, 849-875.
doi: 10.1007/s00030-014-0306-x.![]() ![]() ![]() |