E. Panov

On flows generated by square-integrable vector fields

For square-integrable divergence-free vector field $\boldsymbol{v}$ on $\mathbb{R}^d$ we prove that the following properties are equivalent: 1) the operator $A_0 \rho = \boldsymbol{v} \cdot \nabla \rho$ (where $\rho \in C^\infty_c(\mathbb{R}^d)$) is essentially skew-adjoint on $L^2(\mathbb{R}^d)$; 2) square-integrable...