| Title:
|
A blow-up criterion for the strong solutions to the nonhomogeneous Navier-Stokes-Korteweg equations in dimension three (English) |
| Author:
|
Li, Huanyuan |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
66 |
| Issue:
|
1 |
| Year:
|
2021 |
| Pages:
|
43-55 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper proves a Serrin's type blow-up criterion for the 3D density-dependent Navier-Stokes-Korteweg equations with vacuum. It is shown that if the density $\rho $ and velocity field $u$ satisfy $\|\nabla \rho \|_{L^{\infty }(0,T; W^{1,q})} + \| u\|_{L^s(0,T; L^r_{\omega })}< \infty $ for some $q>3$ and any $(r,s)$ satisfying $2/s+3/r \le 1$, $3 <r \le \infty ,$ then the strong solutions to the density-dependent Navier-Stokes-Korteweg equations can exist globally over $[0,T]$. Here $L^r_{\omega }$ denotes the weak $L^r$ space. (English) |
| Keyword:
|
Navier-Stokes-Korteweg equations |
| Keyword:
|
capillary fluid |
| Keyword:
|
blow-up criterion |
| Keyword:
|
vacuum |
| Keyword:
|
strong solutions |
| MSC:
|
35D35 |
| MSC:
|
35Q35 |
| MSC:
|
76D45 |
| idZBL:
|
07332688 |
| idMR:
|
MR4218601 |
| DOI:
|
10.21136/AM.2020.0228-19 |
| . |
| Date available:
|
2021-01-28T09:58:16Z |
| Last updated:
|
2023-03-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148509 |
| . |
| Reference:
|
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| Reference:
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