Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global weak solutions and asymptotic limits of a Cahn--Hilliard--Darcy
  system modelling tumour growth   We study the existence of weak solutions to a Cahn--Hilliard--Darcy system
coupled with a convection-reaction-diffusion equation through the fluxes,
through the source terms and in Darcy's law. The system of equations arises
from a mixture model for tumour growth accounting for transport mechanisms such
as chemotaxis and active transport. We prove, via a Galerkin approximation, the
existence of global weak solutions in two and three dimensions, along with new
regularity results for the velocity field and for the pressure. Due to the
coupling with the Darcy system, the time derivatives have lower regularity
compared to systems without Darcy flow, but in the two dimensional case we
employ a new regularity result for the velocity to obtain better integrability
and temporal regularity for the time derivatives. Then, we deduce the global
existence of weak solutions for two variants of the model; one where the
velocity is zero and another where the chemotaxis and active transport
mechanisms are absent.

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The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
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The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
3
The categories of this paper are: physics
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The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ph
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph