Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak Continuity and Compactness for Nonlinear Partial Differential
  Equations   We present several examples of fundamental problems involving weak continuity
and compactness for nonlinear partial differential equations, in which
compensated compactness and related ideas have played a significant role. We
first focus on the compactness and convergence of vanishing viscosity solutions
for nonlinear hyperbolic conservation laws, including the inviscid limit from
the Navier-Stokes equations to the Euler equations for homentropy flow, the
vanishing viscosity method to construct the global spherically symmetric
solutions to the multidimensional compressible Euler equations, and the
sonic-subsonic limit of solutions of the full Euler equations for
multidimensional steady compressible fluids. We then analyze the weak
continuity and rigidity of the Gauss-Codazzi-Ricci system and corresponding
isometric embeddings in differential geometry. Further references are also
provided for some recent developments on the weak continuity and compactness
for nonlinear partial differential equations.

25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn