Temperature patches for the subcritical Boussinesq-Navier-Stokes System with no diffusion

Khor, Calvin; Xu, Xin­guang

doi:10.48550/arxiv.2007.14578

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2021

Publication Types

Select...

Other1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 47 publications

(63 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…1 Such a technique may be called as Alinhac's good unknown. One can see [36,37,11,56,40] and reference therein for the application of this method to the 2D Boussinesq system with various partial fractional dissipation. 2 We mention that J.-Y.…”

Section: Introductionmentioning

confidence: 99%

Global regularity of non-diffusive temperature fronts for the 2D viscous Boussinesq system

Chae¹,

Miao²,

Xue³

2021

Preprint

View full text Add to dashboard Cite

In this paper we address the temperature patch problem of the 2D viscous Boussinesq system without heat diffusion term. The temperature satisfies the transport equation and the initial data of temperature is given in the form of non-constant patch, usually called the temperature front initial data. Introducing a good unknown and applying the method of striated estimates, we prove that our partially viscous Boussinesq system admits a unique global regular solution and the initial C k,γ and W 2,∞ regularity of the temperature front boundary with k ∈ Z + = {1, 2, • • • } and γ ∈ (0, 1) will be preserved for all the time. In particular, this naturally extends the previous work by Danchin & Zhang (2017) and Gancedo & García-Juárez (2017). In the proof of the persistence result of higher boundary regularity, we introduce the striated type Besov space B s,ℓ p,r,W (R d ) and establish a series of refined striated estimates in such a function space, which may have its own interest.

show abstract