Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gross-Pitaevskii-Poisson equations for dipolar Bose-Einstein condensate
  with anisotropic confinement   Ground states and dynamical properties of dipolar Bose-Einstein condensate
are analyzed based on the Gross-Pitaevskii-Poisson system (GPPS) and its
dimension reduction models under anisotropic confining potential. We begin with
the three-dimensional (3D) Gross-Pitaevskii-Poisson system and review its
quasi-2D approximate equations when the trap is strongly confined in
$z$-direction and quasi-1D approximate equations when the trap is strongly
confined in $x$-, $y$-directions. In fact, in the quasi-2D equations, a
fractional Poisson equation with the operator $(-\Delta)^{1/2}$ is involved
which brings significant difficulties into the analysis. Existence and
uniqueness as well as nonexistence of the ground state under different
parameter regimes are established for the quasi-2D and quasi-1D equations.
Well-posedness of the Cauchy problem for both equations and finite time blowup
in 2D are analyzed. Finally, we rigorously prove the convergence and linear
convergence rate between the solutions of the 3D GPPS and its quasi-2D and
quasi-1D approximate equations in weak interaction regime.

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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ph
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin