Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A uniqueness result for 3D incompressible fluid-rigid body interaction
  problem   We study a 3D nonlinear moving boundary fluid-structure interaction problem
describing the interaction of the fluid flow with a rigid body. The fluid flow
is governed by 3D incompressible Navier-Stokes equations, while the motion of
the rigid body is described by a system of ordinary differential equations
called Euler equations for the rigid body. The equations are fully coupled via
dynamical and kinematic coupling conditions. We consider two different kinds of
kinematic coupling conditions: no-slip and slip. In both cases we prove a
generalization of the well-known weak-strong uniqueness result for the
Navier-Stokes equations to the fluid-rigid body system. More precisely, we
prove that weak solutions that additionally satisfy Prodi-Serrin $L^r-L^s$
condition are unique in the class of Leray-Hopf weak solutions.

33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics