The transport equation in the scaling invariant Besov or Essén–Janson–Peng–Xiao space.

Abstract This paper addresses a well-posedness of the weak solution to the transport equation (describing how a scalar quantity is transported in a space) with an initial data in the scaling invariant Besov or Essén–Janson–Peng–Xiao space via the boundedness of the left and right compositions acting on each space. [ABSTRACT FROM AUTHOR]