article

Existence and Regularity of the Pressure for the Stochastic Navier---Stokes Equations

Authors:

José A. Langa,

José Real,

Jacques SimonAuthors Info & Claims

Applied Mathematics and Optimization, Volume 48, Issue 3

Pages 195 - 210

https://doi.org/10.1007/s00245-003-0773-7

Published: 01 October 2003 Publication History

Abstract

We prove, on one hand, that for a convenient body force with values in the distribution space (H-1(D))d, where D is the geometric domain of the fluid, there exist a velocity u and a pressure p solution of the stochastic Navier---Stokes equation in dimension 2, 3 or 4. On the other hand, we prove that, for a body force with values in the dual space V' of the divergence free subspace V of (H10(D))d, in general it is not possible to solve the stochastic Navier---Stokes equations. More precisely, although such body forces have been considered, there is no topological space in which Navier---Stokes equations could be meaningful for them.

References

[1]

DaPrato G, Zabczyk J (1992) Stochastic Equations in Infinite Dimensions. Cambridge University Press, Cambridge

Google Scholar

[2]

Lions JL (1965) Problémes aux limites dans les équations aux dérivées partielles. Presses de l'Université de Montreal, Montreal

Google Scholar

[3]

Schwartz L (1973) Théorie des distributions, new edition. Hermann, Paris

Google Scholar

[4]

Simon J (1993) Representation of distributions and explicit antiderivatives up to the boundary. In Progress in Partial Differential Equations: The Metz Surveys 2, M. Chipot ed. Longman, London, pp 201---205

Google Scholar

Cited By

View all

Gao XQin YLi J(2024)Optimally convergent mixed finite element methods for the time-dependent 2D/3D stochastic closed-loop geothermal system with multiplicative noiseAdvances in Computational Mathematics10.1007/s10444-024-10122-x50:3Online publication date: 8-May-2024
https://dl.acm.org/doi/10.1007/s10444-024-10122-x
Doghman J(2024)Numerical approximation of the stochastic Navier–Stokes equations through artificial compressibilityCalcolo: a quarterly on numerical analysis and theory of computation10.1007/s10092-024-00575-361:2Online publication date: 6-Apr-2024
https://dl.acm.org/doi/10.1007/s10092-024-00575-3
Chuyeh Nfor EWoukeng J(2024)On the well-posedness of a stochastic Navier–Stokes–Vlasov–Fokker–Planck systemZeitschrift für Angewandte Mathematik und Physik (ZAMP)10.1007/s00033-024-02327-375:5Online publication date: 1-Oct-2024
https://dl.acm.org/doi/10.1007/s00033-024-02327-3
Show More Cited By

Recommendations

A compact scheme for the streamfunction-velocity formulation of the 2D steady incompressible Navier-Stokes equations in polar coordinaes

A compact difference scheme is developed for the streamfunction-velocity formulation of the steady incompressible Navier---Stokes equations in polar coordinates, which is of second-order accuracy and carries streamfunction and its first derivatives (...
Pressure Gradient method for solving incompressible Navier-Stokes equations with curvilinear coordinate system

A nonstaggered Pressure Gradient (PG) method, one of the finite difference schemes using primitive variables, is applied to solve the 3-D, unsteady incompressible Navier-Stokes equations based on a curvilinear coordinate system. The PG method, in ...
On the Development of a Nonprimitive Navier---Stokes Formulation Subject to Rigorous Implementation of a New Vorticity Integral Condition

In this paper, a new integral vorticity boundary condition has been developed and implemented to compute solution of nonprimitive Navier---Stokes equation. Global integral vorticity condition which is of primitive character can be considered to be of ...

Comments

Information & Contributors

Information

Published In

cover image Applied Mathematics and Optimization

Applied Mathematics and Optimization Volume 48, Issue 3

October 2003

84 pages

ISSN:0095-4616

Issue’s Table of Contents

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 October 2003

Author Tags

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

7
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 08 Feb 2025

Other Metrics

View Author Metrics

Citations

Cited By

View all

Gao XQin YLi J(2024)Optimally convergent mixed finite element methods for the time-dependent 2D/3D stochastic closed-loop geothermal system with multiplicative noiseAdvances in Computational Mathematics10.1007/s10444-024-10122-x50:3Online publication date: 8-May-2024
https://dl.acm.org/doi/10.1007/s10444-024-10122-x
Doghman J(2024)Numerical approximation of the stochastic Navier–Stokes equations through artificial compressibilityCalcolo: a quarterly on numerical analysis and theory of computation10.1007/s10092-024-00575-361:2Online publication date: 6-Apr-2024
https://dl.acm.org/doi/10.1007/s10092-024-00575-3
Chuyeh Nfor EWoukeng J(2024)On the well-posedness of a stochastic Navier–Stokes–Vlasov–Fokker–Planck systemZeitschrift für Angewandte Mathematik und Physik (ZAMP)10.1007/s00033-024-02327-375:5Online publication date: 1-Oct-2024
https://dl.acm.org/doi/10.1007/s00033-024-02327-3
Vo L(2023)Higher Order Time Discretization Method for the Stochastic Stokes Equations with Multiplicative NoiseJournal of Scientific Computing10.1007/s10915-023-02375-397:3Online publication date: 24-Oct-2023
https://dl.acm.org/doi/10.1007/s10915-023-02375-3
Feng XQiu H(2021)Analysis of Fully Discrete Mixed Finite Element Methods for Time-dependent Stochastic Stokes Equations with Multiplicative NoiseJournal of Scientific Computing10.1007/s10915-021-01546-488:2Online publication date: 1-Aug-2021
https://dl.acm.org/doi/10.1007/s10915-021-01546-4
Yamazaki K(2021)Boussinesq System with Partial Viscous Diffusion or Partial Thermal Diffusion Forced by a Random NoiseApplied Mathematics and Optimization10.1007/s00245-021-09756-w84:Suppl 1(1-38)Online publication date: 1-Dec-2021
https://dl.acm.org/doi/10.1007/s00245-021-09756-w
Hausenblas ERandrianasolo T(2019)Time-discretization of stochastic 2-D Navier–Stokes equations with a penalty-projection methodNumerische Mathematik10.1007/s00211-019-01057-3143:2(339-378)Online publication date: 1-Oct-2019
https://dl.acm.org/doi/10.1007/s00211-019-01057-3

Abstract

References

Cited By

Recommendations

A compact scheme for the streamfunction-velocity formulation of the 2D steady incompressible Navier-Stokes equations in polar coordinaes

Pressure Gradient method for solving incompressible Navier-Stokes equations with curvilinear coordinate system

On the Development of a Nonprimitive Navier---Stokes Formulation Subject to Rigorous Implementation of a New Vorticity Integral Condition

Comments

Information

Published In

Publisher

Publication History

Author Tags

Qualifiers

Contributors

Other Metrics

Bibliometrics

Article Metrics

Other Metrics

Citations

Cited By

View options

Share

Share this Publication link

Share on social media

Affiliations