An existence and uniqueness result for the Navier–Stokes type equations on the Heisenberg group

The aim of this paper is to give an existence and uniqueness of solutions for the Cauchy problem of the Navier–Stokes type equations associated to the sublaplacian provided by the left invariant vector fields on the Heisenberg group. To avoid the difficulty of the non-commutative which is intrinsic...

Full description

Saved in:
Bibliographic Details
Published in:Journal of mathematical analysis and applications 2019-05, Vol.473 (1), p.382-407
Main Author: Oka, Yasuyuki
Format: Article
Language:English
Subjects:
Global solution
Heisenberg group
Local solution
Navier–Stokes equations
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The aim of this paper is to give an existence and uniqueness of solutions for the Cauchy problem of the Navier–Stokes type equations associated to 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.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2018.12.056