Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fractional $BV$ solutions for $2\times 2$ systems of conservation laws
  with a linearly degenerate field   The class of $2\times 2$ nonlinear hyperbolic systems with one genuinely
nonlinear field and one linearly degenerate field are considered. Existence of
global weak solutions for small initial data in fractional BV spaces $BV^s$ is
proved. The exponent $s$ is related to the usual fractional Sobolev derivative.
Riemann invariants $w$ and $z$ corresponding respectively to the genuinely
nonlinear component and to the linearly degenerate component play different key
roles in this work. We obtain the existence of a global weak solution provided
that the initial data written in Riemann coordinates $ (w_0,z_0)$ are small in
$ BV^s \times L^\infty $, $1/3 \leq s<1$. The restriction on the exponent $s$
is due to a fundamental result of P.D. Lax, the variation of the Riemann
invariant $z$ on the Lax shock curve depends in a cubic way of the variation of
the other Riemann invariant $w$.

24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin