| Title:
|
A remark on the existence of steady Navier-Stokes flows in 2D semi-infinite channel involving the general outflow condition (English) |
| Author:
|
Morimoto, H. |
| Author:
|
Fujita, H. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
126 |
| Issue:
|
2 |
| Year:
|
2001 |
| Pages:
|
457-468 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider the steady Navier-Stokes equations in a 2-dimensional unbounded multiply connected domain $\Omega $ under the general outflow condition. Let $T$ be a 2-dimensional straight channel $\mathbb{R} \times (-1,1)$. We suppose that $\Omega \cap \lbrace x_1 < 0 \rbrace $ is bounded and that $\Omega \cap \lbrace x_1 > -1 \rbrace = T \cap \lbrace x_1 > -1 \rbrace $. Let $V$ be a Poiseuille flow in $T$ and $\mu $ the flux of $V$. We look for a solution which tends to $V$ as $x_1 \rightarrow \infty $. Assuming that the domain and the boundary data are symmetric with respect to the $x_1$-axis, and that the axis intersects every component of the boundary, we have shown the existence of solutions if the flux is small (Morimoto-Fujita [8]). Some improvement will be reported in this note. We also show certain regularity and asymptotic properties of the solutions. (English) |
| Keyword:
|
stationary Navier-Stokes equations |
| Keyword:
|
non-vanishing outflow |
| Keyword:
|
2-dimensional semi-infinite channel |
| Keyword:
|
symmetry |
| MSC:
|
35B40 |
| MSC:
|
35B65 |
| MSC:
|
35Q30 |
| MSC:
|
76D03 |
| MSC:
|
76D05 |
| idZBL:
|
Zbl 0981.35049 |
| idMR:
|
MR1844283 |
| DOI:
|
10.21136/MB.2001.134017 |
| . |
| Date available:
|
2009-09-24T21:52:42Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134017 |
| . |
| Reference:
|
[1] Amick, C. J.: Steady solutions of the Navier-Stokes equations for certain unbounded channels and pipes.Ann. Scuola Norm. Sup. Pisa 4 (1977), 473–513. MR 0510120 |
| Reference:
|
[2] Amick, C. J.: Properties of steady Navier-Stokes solutions for certain unbounded channel and pipes.Nonlinear Analysis, Theory, Methods & Applications, Vol. 2 (1978), 689–720. MR 0512162, 10.1016/0362-546X(78)90014-7 |
| Reference:
|
[3] Fujita, H.: On the existence and regularity of the steady-state solutions of the Navier-Stokes equation.J. Fac. Sci., Univ. Tokyo, Sec. I 9 (1961), 59–102. Zbl 0111.38502, MR 0132307 |
| Reference:
|
[4] Fujita, H.: On stationary solutions to Navier-Stokes equations in symmetric plane domains under general out-flow condition.Proceedings of International Conference on Navier-Stokes Equations, Theory and Numerical Methods, June 1997, Varenna Italy, Pitman Reseach Notes in Mathematics 388, pp. 16–30. MR 1773581 |
| Reference:
|
[5] Galdi, G. P.: An Introduction to the Mathematical Theory of the Navier-Stokes Equations.Springer, 1994. Zbl 0949.35005 |
| Reference:
|
[6] Ladyzhenskaya, O. A.: The Mathematical Theory of Viscous Incompressible Flow.Gordon and Breach, New York, 1969. Zbl 0184.52603, MR 0254401 |
| Reference:
|
[7] Morimoto, H., Fujita, H.: A remark on existence of steady Navier-Stokes flows in a certain two dimensional infinite tube.Technical Reports Dept. Math., Math-Meiji 99-02, Meiji Univ. |
| Reference:
|
[8] Morimoto, H., Fujita, H.: On stationary Navier-Stokes flows in 2D semi-infinite channel involving the general outflow condition.NSEC7, Ferrara, Italy,. |
| . |
