2019
DOI: 10.1007/s10231-019-00883-4
|View full text |Cite
|
Sign up to set email alerts
|

Bilinear estimates and uniqueness for Navier–Stokes equations in critical Besov-type spaces

Abstract: We show bilinear estimates for the Navier-Stokes equations in critical Besov-weak-Morrey (BWM) spaces that contain the so-called Besov-Morrey (BM) spaces. Our estimates employ only the norm of the natural persistence space and do not use auxiliary norms like, e.g., Kato time-weighted norms. As a corollary, we obtain the uniqueness of mild solutions in the class of continuous functions from [0, ∞) to critical BWM-spaces and, in particular, to BM-spaces. For our purposes, we need to show interpolation properties… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
2
1

Citation Types

0
5
0

Year Published

2021
2021
2024
2024

Publication Types

Select...
5
1

Relationship

1
5

Authors

Journals

citations
Cited by 6 publications
(5 citation statements)
references
References 31 publications
0
5
0
Order By: Relevance
“…In order to estimate the integral terms in (1.3) we present a version in Besov spaces of the Yamazaki estimate obtained in [24] in the context of Lorentz spaces L (p,d) . In the contex of Besov-Lorentz-Morrey spaces and working in the non frational case, a related estimate was proved in [15]. We remark that the estimate presented here is more general and we do not need (although it is possible) to use Lorentz spaces as base space for Besov, and therefore our way of prove is different to that presented in [15].…”
Section: Integral Estimatesmentioning
confidence: 80%
See 2 more Smart Citations
“…In order to estimate the integral terms in (1.3) we present a version in Besov spaces of the Yamazaki estimate obtained in [24] in the context of Lorentz spaces L (p,d) . In the contex of Besov-Lorentz-Morrey spaces and working in the non frational case, a related estimate was proved in [15]. We remark that the estimate presented here is more general and we do not need (although it is possible) to use Lorentz spaces as base space for Besov, and therefore our way of prove is different to that presented in [15].…”
Section: Integral Estimatesmentioning
confidence: 80%
“…In the contex of Besov-Lorentz-Morrey spaces and working in the non frational case, a related estimate was proved in [15]. We remark that the estimate presented here is more general and we do not need (although it is possible) to use Lorentz spaces as base space for Besov, and therefore our way of prove is different to that presented in [15].…”
Section: Integral Estimatesmentioning
confidence: 80%
See 1 more Smart Citation
“…The unconditional uniqueness, that is, the uniqueness of the mild solution is established with a large space of initial data was established for the Keller-Segel (P-E) system on Euclidean space ℝ 𝑛 in a recent work [18]. There are some related works about the unconditional uniqueness theorem for fluid dynamic equations such as Navier-Stokes, Boussinesq equations such as [17,19,20,41]. In this subsection, we establish also an unconditional uniqueness theorem for mild solution of system (3.1) on the hyperbolic space ℍ 𝑛 .…”
Section: Unconditional Uniquenessmentioning
confidence: 99%
“…without invoke Kato's approach, see [13] for weak-Morrey spaces, see [14] for Besovweak-Morrey spaces and see [36] for weak-L p spaces. For stationary Boussinesq equations, see [15] for Besov-weak-Morrey spaces and see [16] for weak-L p spaces.…”
Section: Introductionmentioning
confidence: 99%