The Cauchy problem for the Navier-Stokes type equations on the Heisenberg group (Time-frequency frames and their applications to image processing)

Abstract

The aim of this article is to give a résumé of already published paper [Y. Oka, An existence and uniqueness result for the Navier-Stokes type equations on the Heisenberg group, J. Math. Anal. Appl. 473 (2019), no. 1, 382-407.]. Thus we introduce an existence and uniqueness result of solutions for the Cauchy problem of the Navier-Stokes type equations associated with the sublaplacian provided by the left invariant vector fields on the Heisenberg group. To avoid the difficulty of the non-commutative which is intrinsic in 2-step stratified Lie groups, we construct the solenoidal space by using the right invariant vector fields on the Heisenberg group.