Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the global existence and stability of a three-dimensional supersonic
  conic shock wave   We establish the global existence and stability of a three-dimensional
supersonic conic shock wave for a perturbed steady supersonic flow past an
infinitely long circular cone with a sharp angle. The flow is described by a
3-D steady potential equation, which is multi-dimensional, quasilinear, and
hyperbolic with respect to the supersonic direction. Making use of the
geometric properties of the pointed shock surface together with the
Rankine-Hugoniot conditions on the conic shock surface and the boundary
condition on the surface of the cone, we obtain a global uniform weighted
energy estimate for the nonlinear problem by finding an appropriate multiplier
and establishing a new Hardy-type inequality on the shock surface. Based on
this, we prove that a multi-dimensional conic shock attached to the vertex of
the cone exists globally when the Mach number of the incoming supersonic flow
is sufficiently large. Moreover, the asymptotic behavior of the 3-D supersonic
conic shock solution, that is shown to approach the corresponding background
shock solution in the downstream domain for the uniform supersonic constant
flow past the sharp cone, is also explicitly given.

7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph