Schlatter, A., Struwe, M., Tavildah-Zadeh, A.S.: Global existence of the equivariant Yang-Mills heat flow in four space dimensions, Am. J. Math. 120 (1998), 117--128.  Home/Search   Document Details and Download   Summary   Related Articles

....not blow up. In dimension 4 the situation appears to be even more delicate than the analogous case of the harmonic map heat flow from a 2 dimensional manifold, and the general question of whether blow up can occur remains open; however Schlatter, Struwe and Tahvildah Zadeh have recently shown in [SST] that, under a symmetry Ansatz which is the natural analogue of that that considered in [CDY] solutions to (1.6) will not blow up in finite time. For dimM 5, Naito gave the first proof of finite time blow up, with an approach analogous to that of [CD] he showed Theorem 1.1 ( N, Theorem 1.3] ....

....Paulo Schirmer and Jalal Shatah for helpful discussions. This work was partially supported by SFB288 Differentialgeometrie und Quantenphysik of the DFG (German Research Association) 2 Equivariant connections The situation we consider is similar to that given in [CST, Section 1. 2] cf. also [SST, Section 2], W] in all cases (including the current paper) the authors draw on earlier results of [Du] and [I] 3 We assume that a symmetry group S acts on M , the action fl : S Theta M M being given by (s; x) 7 sx. We further suppose that fl lifts to an action fl on the bundle E, i.e. fl : S Theta ....

Schlatter, A., Struwe, M., Tavildah-Zadeh, A.S.: Global existence of the equivariant Yang-Mills heat flow in four space dimensions, Am. J. Math. 120 (1998), 117--128.

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