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Title: Finite energy global well-posedness of the (3+1)-dimensional Yang-Mills equations using a novel Yang-Mill heat flow gauge
Authors: Oh, Sung-Jin
Advisors: Klainerman, Sergiu
Contributors: Mathematics Department
Keywords: caloric gauge
Yang-Mills equations
Yang-Mills heat flow
Subjects: Mathematics
Issue Date: 2013
Publisher: Princeton, NJ : Princeton University
Abstract: In this thesis, we propose a novel choice of gauge for the Yang-Mills equations on the Minkowski space $\mathbb{R}^{1+d}$. A crucial ingredient is the associated Yang-Mills heat flow. Unlike the previous approaches, the new gauge is applicable for large data, while the special analytic structure of the Yang-Mills equations is still manifest. As the first application of the new approach, we shall give new proofs of $H^{1}_{x}$ local well-posedness and finite energy global well-posedness of the Yang-Mills equations on $\mathbb{R}^{1+3}$. These are classical results first proved by S. Klainerman and M. Machedon using the method of local Coulomb gauges, which had been difficult to extend to other settings. As our approach does not possess its drawbacks (in particular the use of Uhlenbeck's lemma is avoided), it is expected to be more robust and easily applicable to other problems
Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog
Type of Material: Academic dissertations (Ph.D.)
Language: en
Appears in Collections:Mathematics

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