On continuation criteria for the full compressible Navier-Stokes equations in Lorentz spaces Article Swipe

MAKE IMPACT

Yan Qing Wang , Wei Wei , Gang Wu , Yulin Ye · YOU? · · 2019 · Open Access · · DOI: https://doi.org/10.48550/arxiv.1912.11854

In this paper, we derive several new sufficient conditions of non-breakdown of strong solutions for for both the 3D heat-conducting compressible Navier-Stokes system and nonhomogeneous incompressible Navier-Stokes equations. First, it is shown that there exists a positive constant $\varepsilon$ such that the solution $(ρ,u,θ)$ to full compressible Navier-Stokes equations can be extended beyond $t=T$ provided that one of the following two conditions holds (1) $ρ\in L^{\infty}(0,T;L^{\infty}(\mathbb{R}^{3}))$, $u\in L^{p,\infty}(0,T;L^{q,\infty}(\mathbb{R}^{3}))$ and $$\| u\|_{L^{p,\infty}(0,T;L^{q,\infty}(\mathbb{R}^{3}))}\leq \varepsilon, ~~\text{with}~~ {2/p}+ {3/q}=1,\ \ q>3;$$ (2) $λ<3μ,$ $ρ\in L^{\infty}(0,T;L^{\infty}(\mathbb{R}^{3}))$, $θ\in L^{p,\infty}(0,T;L^{q,\infty}(\mathbb{R}^{3}))$ and $$\|θ\|_{L^{p,\infty}(0,T; L^{q,\infty}(\mathbb{R}^{3}))}\leq \varepsilon, ~~\text{with}~~ {2/p}+ {3/q}=2,\ \ q>3/2.$$ To the best of our knowledge, this is the first continuation theorem allowing the time direction to be in Lorentz spaces for the compressible fluid. Second, we establish some blow-up criteria in anisotropic Lebesgue spaces to the full Navier-Stokes system. Third, without the condition on $ρ$ in (0.1) and (0.3), the results also hold for the 3D nonhomogeneous incompressible Navier-Stokes equations. The appearance of vacuum in these systems could be allowed.

Type

preprint

Language

en

Landing Page

http://arxiv.org/abs/1912.11854

PDF

https://arxiv.org/pdf/1912.11854

OA Status

green

References

34

Related Works

10

OpenAlex ID

https://openalex.org/W2997815767

Raw OpenAlex JSON

OpenAlex ID

https://openalex.org/W2997815767

Canonical identifier for this work in OpenAlex

DOI

https://doi.org/10.48550/arxiv.1912.11854

Digital Object Identifier

Title

On continuation criteria for the full compressible Navier-Stokes equations in Lorentz spaces

Work title

Type

preprint

OpenAlex work type

Language

en

Primary language

Publication year

2019

Year of publication

Publication date

2019-12-26

Full publication date if available

Authors

Yan Qing Wang, Wei Wei, Gang Wu, Yulin Ye

List of authors in order

Landing page

https://arxiv.org/abs/1912.11854

Publisher landing page

PDF URL

https://arxiv.org/pdf/1912.11854

Direct link to full text PDF

Open access

Yes

Whether a free full text is available

OA status

green

Open access status per OpenAlex

OA URL

https://arxiv.org/pdf/1912.11854

Direct OA link when available

Concepts

Navier–Stokes equations, Compressibility, Physics, Mathematical physics, Lorentz transformation, Mathematical analysis, Mathematics, Combinatorics, Quantum mechanics, Thermodynamics

Top concepts (fields/topics) attached by OpenAlex

Cited by

0

Total citation count in OpenAlex

References (count)

34

Number of works referenced by this work

Related works (count)

10

Other works algorithmically related by OpenAlex

Full payload