On global solutions to a defocusing semi-linear wave equation
Gallagher, Isabelle ; Planchon, Fabrice
Rev. Mat. Iberoamericana, Tome 19 (2003) no. 2, p. 161-177 / Harvested from Project Euclid
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We prove that the 3D cubic defocusing semi-linear wave equation is globally well-posed for data in the Sobolev space $\dot{H}^{s}$ where $s>3/4$. This result was obtained in [Kenig-Ponce-Vega, 2000] following Bourgain's method ([Bourgain, 1998]). We present here a different and somewhat simpler argument, inspired by previous work on the Navier-Stokes equations ([Calderon, 1990], [Gallagher-Planchon, 2002])
Publié le : 2003-03-15
Classification:  Wave equation,  Global solution,  35L70,  35L05 
@article{1049123083,
     author = {Gallagher, Isabelle and Planchon, Fabrice},
     title = {On global solutions to a defocusing semi-linear wave
 equation},
     journal = {Rev. Mat. Iberoamericana},
     volume = {19},
     number = {2},
     year = {2003},
     pages = { 161-177},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1049123083}
}

Gallagher, Isabelle; Planchon, Fabrice. On global solutions to a defocusing semi-linear wave
 equation. Rev. Mat. Iberoamericana, Tome 19 (2003) no. 2, pp.  161-177. http://gdmltest.u-ga.fr/item/1049123083/