The gauge-invariant I-method for Yang-Mills
A talk in the Oberseminar Analysis series by
Cristian Gavrus
| Abstract: | In this talk we discuss the global well-posedness of the 3d Yang-Mills equation in the temporal gauge for regularities below the energy. Unlike related equations, Yang-Mills is not directly amenable to the method of almost conservation laws (I-method) in its Fourier and global version. We discuss a modified energy which: (1) Is gauge-invariant and easy to localize (2) Provides local gauges which give control of local Sobolev norms (3) Is slightly smoother in time compared to the classical I-method energy for related systems. The spatial smoothing is realized via the Yang-Mills heat flow instead of the multiplier I. The local gauge selection is compatible with recent initial data extension results. Therefore, smoothened energy differences can be partitioned into local pieces whose (appropriately extended) bounds can be square summed. Zoom Meeting ID: 986 0677 6055 Passcode: 430747 $\href{https://uni-bielefeld.zoom.us/j/98606776055?pwd=azBFdUVaQnJMU01tWjZUVEdxN2x5Zz09}{\textbf{Join Zoom Meeting}}$ Within the CRC this talk is associated to the project(s): A1 |