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

By José A. Langa, José Real, J. Simon. 2003

55 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Computational Mechanics, Finance

View Paper: https://www.semanticscholar.org/paper/cda289043815a7528f46460d6a2496166468297c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Tomás Caraballo
2. José Real
3. Takeshi Taniguchi
4. Pedro Marín-Rubio
5. Bixiang Wang
6. Linfang Liu
7. Xiaoying Han
8. Marco Romito

In Computational Mechanics

1. Tomás Caraballo
2. Takeshi Taniguchi
3. José Real

In Finance

1. Tomás Caraballo
2. Takeshi Taniguchi
3. José Real

Citations in the corpus

• On the existence and uniqueness of solutions to stochastic three-dimensional Lagrangian averaged Navier–Stokes equations (2006, methodology): “Also, as u ∈ L4(Ω,F , P ; C([0, T ];V )), and is Ft-progressively measurable, then it follows that F (t, u) ∈ L4(Ω,Ft, P ; L2(0, t; (H−1(D))3)), and reasoning as in Langa et al. (2003), one also obtains G(t, u)Ẇt ∈ L4(Ω,Ft, P ; W−1,∞(0, t; (L2(D)3))), for all t ∈ [0, T ].”