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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Global existence for $ 1$D, compressible, isentropic Navier-Stokes equations with large initial data

Author: David Hoff
Journal: Trans. Amer. Math. Soc. 303 (1987), 169-181
MSC: Primary 35Q10; Secondary 76D05
MathSciNet review: 896014
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Abstract: We prove the global existence of weak solutions of the Cauchy problem for the Navier-Stokes equations of compressible, isentropic flow of a polytropic gas in one space dimension. The initial velocity and density are assumed to be in $ {L^2}$ and $ {L^2} \cap BV$ respectively, modulo additive constants. In particular, no smallness assumptions are made about the intial data. In addition, we prove a result concerning the asymptotic decay of discontinuities in the solution when the adiabatic constant exceeds $ 3/2$.

References [Enhancements On Off] (What's this?)

  • [1] David Hoff, Construction of solutions for compressible, isentropic Navier-Stokes equations in one space dimension with nonsmooth initial data, Proc. Roy. Soc. Edinburgh Sect. A 103 (1986), no. 3-4, 301–315. MR 866843 (88b:35156),
  • [2] David Hoff and Tai-Ping Liu, (to appear).
  • [3] David Hoff and Joel Smoller, Solutions in the large for certain nonlinear parabolic systems, Ann. Inst. H. Poincaré Anal. Non Linéaire 2 (1985), no. 3, 213–235 (English, with French summary). MR 797271 (87b:35078)
  • [4] A. V. Kazhikhov and V. V. Shelukhin, Unique global solution with respect to time of initial-boundary value problems for one-dimensional equations of a viscous gas, Prikl. Mat. Meh. 41 (1977), no. 2, 282–291 (Russian); English transl., J. Appl. Math. Mech. 41 (1977), no. 2, 273–282. MR 0468593 (57 #8425)
  • [6] Jong Uhn Kim, Global existence of solutions of the equations of one-dimensional thermoviscoelasticity with initial data in 𝐵𝑉 and 𝐿¹, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 10 (1983), no. 3, 357–427. MR 739917 (85k:35210)
  • [7] Denis Serre, Solutions faibles globales des équations de Navier-Stokes pour un fluide compressible, C. R. Acad. Sci. Paris Sér. I Math. 303 (1986), no. 13, 639–642 (French, with English summary). MR 867555 (88a:35193)

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PII: S 0002-9947(1987)0896014-6
Article copyright: © Copyright 1987 American Mathematical Society

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