Initial behavior of solutions to the Yang–Mills heat equation
| Autor: | Charalambous, N., Gross, L. |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Weakly parabolic
Applied Mathematics Heat equation 010102 general mathematics Regular polygon Yang–Mills existence and mass gap Curvature 01 natural sciences Yang–Mills Infinite covariant differentiability Gauge groups Norm (mathematics) Bounded function 0103 physical sciences Initial value problem Gaffney–Friedrichs inequality 010307 mathematical physics 0101 mathematics Analysis Mathematics Mathematical physics |
| Zdroj: | Journal of Mathematical Analysis and Applications J.Math.Anal.Appl. |
| Popis: | We explore the small-time behavior of solutions to the Yang–Mills heat equation with rough initial data. We consider solutions A ( t ) with initial value A 0 ∈ H 1 / 2 ( M ) , where M is a bounded convex region in R 3 or all of R 3 . The behavior, as t ↓ 0 , of the L p ( M ) norms of the time derivatives of A ( t ) and its curvature B ( t ) will be determined for p = 2 and 6, along with the H 1 ( M ) norm of these derivatives. |
| Databáze: | OpenAIRE |
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