Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic stability of precessing domain walls for the
  Landau-Lifshitz-Gilbert equation in a nanowire with Dzyaloshinskii-Moriya
  interaction   We consider a ferromagnetic nanowire and we focus on an asymptotic regime
where the Dzyaloshinskii-Moriya interaction is taken into account. First we
prove a dimension reduction result via $\Gamma$-convergence that determines a
limit functional $E$ defined for maps $m:\mathbb{R}\to \mathbb{S}^2$ in the
direction $e_1$ of the nanowire. The energy functional $E$ is invariant under
translations in $e_1$ and rotations about the axis $e_1$. We fully classify the
critical points of finite energy $E$ when a transition between $-e_1$ and $e_1$
is imposed; these transition layers are called (static) domain walls. The
evolution of a domain wall by the Landau-Lifshitz-Gilbert equation associated
to $E$ under the effect of an applied magnetic field $h(t)e_1$ depending on the
time variable $t$ gives rise to the so-called precessing domain wall. Our main
result proves the asymptotic stability of precessing domain walls for small $h$
in $L^\infty([0, +\infty))$ and small $H^1(\mathbb{R})$ perturbations of the
static domain wall, up to a gauge which is intrinsic to invariances of the
functional $E$.

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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio