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Optimal results for the nonhomogeneous initial-boundary value problem for the two-dimensional Navier-Stokes equations

Fontes, Magnus LU (2010) In Journal of Mathematical Fluid Mechanics 12. p.412-434
Abstract
In this work we study the fully nonhomogeneous initial boundary value problem for the two-dimensional time-dependent Navier–Stokes equations in a general open space domain in R2 with low regularity assumptions on the initial and the boundary value data. We show that the perturbed Navier–Stokes operator is a diffeomorphism from a suitable function space onto its own dual and as a corollary we get that the Navier–Stokes equations are uniquely solvable in these spaces and that the solution depends smoothly on all involved data. Our source data space and solution space are in complete natural duality and in this sense, without any smallness assumptions on the data, we solve the equations for data with optimally low regularity in both space and... (More)
In this work we study the fully nonhomogeneous initial boundary value problem for the two-dimensional time-dependent Navier–Stokes equations in a general open space domain in R2 with low regularity assumptions on the initial and the boundary value data. We show that the perturbed Navier–Stokes operator is a diffeomorphism from a suitable function space onto its own dual and as a corollary we get that the Navier–Stokes equations are uniquely solvable in these spaces and that the solution depends smoothly on all involved data. Our source data space and solution space are in complete natural duality and in this sense, without any smallness assumptions on the data, we solve the equations for data with optimally low regularity in both space and time. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Navier–Stokes, perturbed, nonhomogeneous boundary condition, anisotropic Beppo–Levi space, time-dependent
in
Journal of Mathematical Fluid Mechanics
volume
12
pages
412 - 434
publisher
Birkhaüser
external identifiers
  • wos:000281041600006
  • scopus:77955921401
ISSN
1422-6928
DOI
10.1007/s00021-009-0296-3
language
English
LU publication?
yes
id
4f20efb9-0067-4fbc-b15a-b50a4697d52c (old id 1470840)
date added to LUP
2009-09-02 08:14:25
date last changed
2018-05-29 10:44:33
@article{4f20efb9-0067-4fbc-b15a-b50a4697d52c,
  abstract     = {In this work we study the fully nonhomogeneous initial boundary value problem for the two-dimensional time-dependent Navier–Stokes equations in a general open space domain in R2 with low regularity assumptions on the initial and the boundary value data. We show that the perturbed Navier–Stokes operator is a diffeomorphism from a suitable function space onto its own dual and as a corollary we get that the Navier–Stokes equations are uniquely solvable in these spaces and that the solution depends smoothly on all involved data. Our source data space and solution space are in complete natural duality and in this sense, without any smallness assumptions on the data, we solve the equations for data with optimally low regularity in both space and time.},
  author       = {Fontes, Magnus},
  issn         = {1422-6928},
  keyword      = {Navier–Stokes,perturbed,nonhomogeneous boundary condition,anisotropic Beppo–Levi space,time-dependent},
  language     = {eng},
  pages        = {412--434},
  publisher    = {Birkhaüser},
  series       = {Journal of Mathematical Fluid Mechanics},
  title        = {Optimal results for the nonhomogeneous initial-boundary value problem for the two-dimensional Navier-Stokes equations},
  url          = {http://dx.doi.org/10.1007/s00021-009-0296-3},
  volume       = {12},
  year         = {2010},
}