scholarly journals Global weak solutions of the Teichmüller harmonic map flow into general targets

2019 ◽  
Vol 12 (3) ◽  
pp. 815-842 ◽  
Author(s):  
Melanie Rupflin ◽  
Peter M. Topping
Keyword(s):  
Weak Solutions ◽  
Harmonic Map ◽  
Global Weak Solutions ◽  
Harmonic Map Flow

Weak solutions for the time fractional harmonic map flow

2020 ◽  
Vol 196 ◽  
pp. 111772
Author(s):  
Yan-Hong Chen ◽  
Youquan Zheng
Keyword(s):  
Weak Solutions ◽  
Harmonic Map ◽  
Harmonic Map Flow

Non-Uniqueness for the p-Harmonic Flow

1997 ◽  
Vol 40 (2) ◽  
pp. 174-182 ◽  
Author(s):  
Norbert Hungerbühler
Keyword(s):  
Weak Solutions ◽  
Boundary Data ◽  
Harmonic Maps ◽  
Harmonic Map ◽  
Smooth Domain ◽  
Global Weak Solutions ◽  
Bounded Smooth Domain ◽  
Harmonic Flow ◽  
Bounded Smooth

AbstractIf f0: Ω ⊂ ℝm → Sn is a weakly p-harmonic map from a bounded smooth domain Ω in ℝm (with 2 < p < m) into a sphere and if f0 is not stationary p-harmonic, then there exist infinitely many weak solutions of the p-harmonic flow with initial and boundary data f0, i.e., there are infinitely many global weak solutions f :Ω × ℝ → ⊂ Sn ofWe also show that there exist non-stationary weakly (m − 1)-harmonic maps f0: Bm → Sm−1.

Infinite time blow-up for half-harmonic map flow from R into S1

2021 ◽  
Vol 143 (4) ◽  
pp. 1261-1335
Author(s):  
Yannick Sire ◽  
Juncheng Wei ◽  
Youquan Zheng
Keyword(s):  
Blow Up ◽  
Harmonic Map ◽  
Infinite Time ◽  
Harmonic Map Flow

scholarly journals Uniqueness and nonuniqueness of limits of Teichmüller harmonic map flow

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
James Kohout ◽  
Melanie Rupflin ◽  
Peter M. Topping
Keyword(s):  
Constant Curvature ◽  
Harmonic Map ◽  
Gradient Flow ◽  
Minimal Immersion ◽  
Curvature Surface ◽  
Previous Theory ◽  
Target Manifold ◽  
Harmonic Map Flow

AbstractThe harmonic map energy of a map from a closed, constant-curvature surface to a closed target manifold can be seen as a functional on the space of maps and domain metrics. We consider the gradient flow for this energy. In the absence of singularities, previous theory established that the flow converges to a branched minimal immersion, but only at a sequence of times converging to infinity, and only after pulling back by a sequence of diffeomorphisms. In this paper, we investigate whether it is necessary to pull back by these diffeomorphisms, and whether the convergence is uniform as {t\to\infty}.

scholarly journals Moving mesh for the axisymmetric harmonic map flow

2005 ◽  
Vol 39 (4) ◽  
pp. 781-796
Author(s):  
Benoit Merlet ◽  
Morgan Pierre
Keyword(s):  
Harmonic Map ◽  
Moving Mesh ◽  
Harmonic Map Flow
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