Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local Well-Posedness of the Gravity-Capillary Water Waves System in the
  Presence of Geometry and Damping   We consider the gravity-capillary water waves problem in a domain $\Omega_t
\subset \mathbb{T} \times \mathbb{R}$ with substantial geometric features.
Namely, we consider a variable bottom, smooth obstacles in the flow and a
constant background current. We utilize a vortex sheet model introduced by
Ambrose, et. al. in arXiv:2108.01786. We show that the water waves problem is
locally-in-time well-posed in this geometric setting and study the lifespan of
solutions. We then add a damping term and derive evolution equations that
account for the damper. Ultimately, we show that the same well-posedness and
lifespan results apply to the damped system. We primarily utilize energy
methods.

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The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys