English

Initial behavior of solutions to the Yang-Mills heat equation

Mathematical Physics 2016-09-20 v1 Analysis of PDEs math.MP

Abstract

We explore the small-time behavior of solutions to the Yang-Mills heat equation with rough initial data. We consider solutions A(t)A(t) with initial value A0H1/2(M)A_0\in H_{1/2}(M), where MM is a bounded convex region in R3\mathbb{R}^3 or all of R3\mathbb{R}^3. The behavior, as t0t\downarrow 0, of the Lp(M)L^p(M) norms of the time derivatives of A(t)A(t) and its curvature B(t)B(t) will be determined for p=2p=2 and 66, along with the H1(M)H_1(M) norm of these derivatives.

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Cite

@article{arxiv.1609.05607,
  title  = {Initial behavior of solutions to the Yang-Mills heat equation},
  author = {Nelia Charalambous and Leonard Gross},
  journal= {arXiv preprint arXiv:1609.05607},
  year   = {2016}
}

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46 pages