2016
DOI: 10.1007/s00205-016-0979-x
|View full text |Cite
|
Sign up to set email alerts
|

Global Strong Well-Posedness of the Three Dimensional Primitive Equations in $${L^p}$$ L p -Spaces

Abstract: Abstract. In this article, an L p -approach to the primitive equations is developed. In particular, it is shown that the three dimensional primitive equations admit a unique, global strong solution for all initial data a ∈ [Xp, D(Ap)] 1/p provided p ∈ [6/5, ∞). To this end, the hydrostatic Stokes operator Ap defined on Xp, the subspace of L p associated with the hydrostatic Helmholtz projection, is introduced and investigated. Choosing p large, one obtains global well-posedness of the primitive equations for s… Show more

Help me understand this report
View preprint versions

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
2
1

Citation Types

1
137
0
3

Year Published

2016
2016
2020
2020

Publication Types

Select...
4
3

Relationship

2
5

Authors

Journals

citations
Cited by 82 publications
(141 citation statements)
references
References 34 publications
1
137
0
3
Order By: Relevance
“…Taking advantage of the regularization of solutions for t > 0 one passes into the setting discussed in [11] and [9], and thus we obtain the following corollary. Our main result on the hydrostatic semigroup acting on X σ reads as follows.…”
Section: Resultsmentioning
confidence: 85%
See 3 more Smart Citations
“…Taking advantage of the regularization of solutions for t > 0 one passes into the setting discussed in [11] and [9], and thus we obtain the following corollary. Our main result on the hydrostatic semigroup acting on X σ reads as follows.…”
Section: Resultsmentioning
confidence: 85%
“…Our first main result concerns the global well-posedness of the primitive equations for arbitrarily large initial data in X σ , while the second result extends this situation to the case of small perturbations in L ∞ H L p z (Ω). Here, a strong solution means -as in [11] -a solution v to the primitive equations satisfying…”
Section: Resultsmentioning
confidence: 99%
See 2 more Smart Citations
“…We are interested in time-global error estimates for finite element approximations of the hydrostatic Stokes and the primitive equations. In contrast to the three-dimensional Navier-Stokes equations, it is known that the three-dimensional primitive equations are globally well-posed in the L p -settings (see [2] for p = 2, and [19] for p ∈ (1, ∞)). In their proofs, the analyticity of the hydrostatic Stokes semigroup plays a crucial role.…”
Section: Introductionmentioning
confidence: 99%