Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On one criterion of the uniqueness of generalized solutions for linear
  transport equations with discontinuous coefficients   We study generalized solutions of multidimensional transport equation with
bounded measurable solenoidal field of coefficients $a(x)$. It is shown that
any generalized solution satisfies the renormalization property if and only if
the operator $a\cdot\nabla u$, $u\in C_0^1(\mathbb{R}^n)$ in the Hilbert space
$L^2(\mathbb{R}^n)$ is an essentially skew-adjoint operator, and this is
equivalent to the uniqueness of generalized solutions. We also establish
existence of a contractive semigroup, which provides generalized solutions, and
give a criterion of its uniqueness.

31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs