Remarks on the asymptotic behaviour of solutions to the compressible Navier–Stokes equations in the half-line
2002 ◽
Vol 132
(3)
◽
pp. 627-638
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Keyword(s):
We study the time-asymptotic behaviour of solutions to the Navier-Stokes equations for a one-dimensional viscous polytropic ideal gas in the half-line. Using a local representation for the specific volume, which is obtained by using a special cut-off function to localize the problem, and the weighted energy estimates, we prove that the specific volume is pointwise bounded from below and above for all x, t and that for all t the temperature is bounded from below and above locally in x. Moreover, global solutions are convergent as time goes to infinity. The large-time behaviour of solutions to the Cauchy problem is also examined.
2002 ◽
Vol 132
(03)
◽
pp. 627
2011 ◽
Vol 27
(4)
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pp. 697-712
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2000 ◽
Vol 330
(5)
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pp. 427-432
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1996 ◽
Vol 45
(4)
◽
pp. 0-0
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1969 ◽
Vol s1-44
(1)
◽
pp. 340-346
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2017 ◽
Vol 34
(2)
◽
pp. 277-291
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2017 ◽
Vol 40
(18)
◽
pp. 7425-7437
Keyword(s):