Sur les applications harmoniques

Geometric Renormalization Below the Ground State

“…See Lin-Wang [10] for work on convergence of sequences of heat flows. For the consideration of noncompact target manifolds, see Mitteau [13], Li-Tam [8], and the references therein. The book [11] by Lin-Wang provides an extensive (though not exhaustive) survey.…”

Magnetization switching in small ferromagnetic ellipsoidal samples

“…Although the equations look quite similar, the gyromagnetic term in the magnetic model make them very different from the point of view of mathematical analysis. Indeed, a lot more results are known in the more geometrical case of the harmonic maps equation, like explicit blow-up solutions in finite time [7,9], global regular solutions if the energy is small [17] or if the energy is non-increasing in time [11], or if the initial condition takes values in a open half-sphere [13], etc. Non-uniqueness results are known for the heat flow of harmonic maps [8] or for Landau-Lifschitz equations but only when the effective magnetic field consists of the exchange term [1].…”

Magnetization switching on small ferromagnetic ellipsoidal samples

“…Although the equations look quite similar, the gyromagnetic term in the magnetic model make them very different from the point of view of mathematical analysis. Indeed, a lot more results are known in the more geometrical case of the harmonic maps equation, like explicit blow-up solutions in finite time [7,9], global regular solutions if the energy is small [17] or if the energy is non-increasing in time [11], or if the initial…”