Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Compressible fluids interacting with 3D visco-elastic bulk solids   We consider the physical setup of a three-dimensional fluid-structure
interaction problem. A viscous compressible gas or liquid interacts with a
nonlinear, visco-elastic, three-dimensional bulk solid. The latter is described
by a hyperbolic evolution with a non-convex elastic energy functional. The
fluid is modelled by the compressible Navier--Stokes equations with a
barotropic pressure law. Due to the motion of the solid, the fluid domain is
time-changing. Our main result is the long-time existence of a weak solution to
the coupled system until the time of a collision. The nonlinear coupling
between the motions of the two different matters is established via the method
of minimising movements. The motion of both the solid and the fluid is chosen
via an incrimental minimization with respect to dissipative and static
potentials. These variational choices together with a careful construction of
an underlying flow map for our approximation then directly result in the
pressure gradient and the material time derivatives.

30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat