Stable self-similar blowup in the supercritical heat flow of harmonic maps

Stable Exponentially Harmonic Maps Between Finsler Manifolds

stable exponentially harmonic maps between finsler manifolds

On uniqueness of heat flow of harmonic maps

In this paper, we establish the uniqueness of heat flow of harmonic maps into (N,h) that have sufficiently small renormalized energies, provided that N is either a unit sphere Sk−1 or a Riemannian homogeneous manifold. For such a class of solutions, we also establish the convexity property of the Dirichlet energy for t ≥ t0 > 0 and the unique limit property at time infinity. As a corollary, the...

the effects of changing roughness on the flow structure in the bends

flow in natural river bends is a complex and turbulent phenomenon which affects the scour and sedimentations and causes an irregular bed topography on the bed. for the reason, the flow hydralics and the parameters which affect the flow to be studied and understand. in this study the effect of bed and wall roughness using the software fluent discussed in a sharp 90-degree flume bend with 40.3cm ...

On the uniqueness of heat flow of harmonic maps and hydrodynamic flow of nematic liquid crystals

For any n-dimensional compact Riemannian manifold (M, g) without boundary and another compact Riemannian manifold (N,h), we establish the uniqueness of the heat flow of harmonic maps from M to N in the class C([0, T ),W ). For the hydrodynamic flow (u, d) of nematic liquid crystals in dimensions n = 2 or 3, we show the uniqueness holds for the class of weak solutions provided either (i) for n =...