Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global well-posedness of the spatially homogeneous Hubbard-Boltzmann
  equation   The Hubbard model is a simplified description for the evolution of
interacting spin-1/2 fermions on a d-dimensional lattice. In a kinetic scaling
limit, the Hubbard model can be associated with a matrix-valued Boltzmann
equation, the Hubbard-Boltzmann equation. Its collision operator is a sum of
two qualitatively different terms: The first term is similar to the collision
operator of the fermionic Boltzmann-Nordheim equation. The second term leads to
a momentum-dependent rotation of the spin basis. The rotation is determined by
a principal value integral which depends quadratically on the state of the
system and might become singular for non-smooth states. In this paper, we prove
that the spatially homogeneous equation nevertheless has global solutions in
L^\infty(T^d,C^{2x2}) for any initial data W_0 which satisfies the "Fermi
constraint" in the sense that 0 <= W_0 <= 1 almost everywhere. We also prove
that there is a unique "physical" solution for which the Fermi constraint holds
at all times. For the proof, we need to make a number of assumptions about the
lattice dispersion relation which, however, are satisfied by the nearest
neighbor Hubbard model, provided that d >= 3. These assumptions suffice to
guarantee that, although possibly singular, the local rotation term is
generated by a function in L^2(T^d,C^{2x2}).

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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: q-bio
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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: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph