| Title:
|
Asymptotic behavior of the solutions to a one-dimensional motion of compressible viscous fluids (English) |
| Author:
|
Yanagi, Shigenori |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
120 |
| Issue:
|
4 |
| Year:
|
1995 |
| Pages:
|
431-443 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study the one-dimensional motion of the viscous gas represented by the system $v_t-u_x = 0$, $ u_t+ p(v)_x = \mu(u_x/v)_x + f \left( \int_0^xv\dd x,t \right)$, with the initial and the boundary conditions $(v(x,0), u(x,0)) = (v_0(x), u_0(x))$, $u(0,t) = u(X,t) = 0$. We are concerned with the external forces, namely the function $f$, which do not become small for large time $t$. The main purpose is to show how the solution to this problem behaves around the stationary one, and the proof is based on an elementary $L^2$-energy method. (English) |
| Keyword:
|
asymptotic behavior of solutions |
| Keyword:
|
one-dimensional motion of the viscous gas |
| Keyword:
|
compressible viscous gas |
| MSC:
|
35B40 |
| MSC:
|
35Q30 |
| MSC:
|
35Q35 |
| MSC:
|
76N10 |
| MSC:
|
76N15 |
| idZBL:
|
Zbl 0845.35084 |
| idMR:
|
MR1415090 |
| DOI:
|
10.21136/MB.1995.126088 |
| . |
| Date available:
|
2009-09-24T21:13:51Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126088 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
|
[7] A. V. Kazhikhov, V. B. Nikolaev: On the correctness of boundary value problems for the equations of a viscous gas with a non-monotonic function of state.Chislennye Metody Mekh. Sploshnoi Sredy 10 (1979), 77-84. (In Russian.) MR 0558830 |
| Reference:
|
[8] A. V. Kazhikhov, V. B. Nikolaev: On the theory of the Navier-Stokes equations of a viscous gas with nonmonotone state function.Soviet Math. Dokl. 20 (1979), 583-585. Zbl 0424.35074 |
| Reference:
|
[9] A. V. Kazhikhov, V. V. Shelukhin: Unique global solution with respect to time of initial-boundary value problems for one-dimensional equations of a viscous gas.J. Appl. Math. Mech. 41 (1977)), 273-282. Zbl 0393.76043, MR 0468593, 10.1016/0021-8928(77)90011-9 |
| Reference:
|
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| Reference:
|
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| Reference:
|
[12] V. A. Solonnikov, A. V. Kazhikhov: Existence theorems for the equations of motion of a compressible viscous fluid.Ann. Rev. Fluid Mech. 13 (1981), 79-95. Zbl 0492.76074, 10.1146/annurev.fl.13.010181.000455 |
| Reference:
|
[13] A. Tani: A survey on the one-dimensional compressible isentropic Navier-Stokes equations in a field of external forces.(unpublished). |
| Reference:
|
[14] S. Yanagi: Global existence for one-dimensional motion of non-isentropic viscous fluids.Math. Methods in Appl. Sci. 16 (1993), 609-624. Zbl 0780.35082, MR 1240450, 10.1002/mma.1670160902 |
| Reference:
|
[15] A. A. Zlotnik: On equations for one-dimensional motion of a viscous barotropic gas in the presence of a body force.Sibir. Mat. Zh. 33 (1993), 62-79. |
| . |
