Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence of weak solutions to a generalized nonlinear multi-layered
  fluid-structure interaction problem with the Navier-slip boundary conditions   We consider a fluid-structure interaction problem with Navier-slip boundary
conditions in which the fluid is considered as a non-Newtonian fluid and the
structure is described by a nonlinear multi-layered model. The fluid domain is
driven by a nonlinear elastic shell and thus is not fixed. To simplify the
problem, we map the moving fluid domain into a fixed domain by applying an
arbitrary Lagrange Euler mapping. Unlike the classical method by which we can
consider the problem as its entirety, we utilize the time-discretization and
split the problem into a fluid subproblem and a structure subproblem by an
operator splitting scheme. Since the structure subproblem is nonlinear,
Lax-Milgram lemma does not hold. Here we prove the existence and uniqueness by
means of the traditional semigroup theory. Noticing that the Non-Newtonian
fluid possesses a $ p- $Laplacian structure, we show the existence and
uniqueness of solutions to the fluid subproblem by considering the
Browder-Minty theorem. With the uniform energy estimates, we deduce the weak
and weak* convergence respectively. By a generalized Aubin-Lions-Simon Lemma
proposed by Muha and Cani\'c [J. Differential Equations {\bf 266} (2019),
8370--8418], we obtain the strong convergence. Finally, we construct the test
functions and pass the approximate weak formulation to the limit as time step
goes to zero with the convergence results.

7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th