Global regularity and scattering for general non-linear wave equations II. (4+1) dimensional Yang-Mills equations in the Lorentz gauge

• Autores: Jacob Sterbenz
• Localización: American journal of mathematics, ISSN 0002-9327, Vol. 129, Nº 3, 2007, págs. 611-664
• Idioma: inglés
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• Resumen

  • We continue here with previous investigations on the global behavior of general type nonlinear wave equations for a class of small, scale-invariant initial data. In particular, we show that the (4 + 1) dimensional Yang-Mills equations are globally well posed with asymptotically free behavior for a wide class of initial data sets which include general charges. The method here is based on the use of a new set of Strichartz estimates for the linear wave equation which incorporates extra weighted smoothness assumptions with respect to the angular variable, along with the construction of appropriate micro-local function spaces which take into account this type of additional regularity.