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Transactions of the American Mathematical Society

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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$.

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Article copyright: © Copyright 1987 American Mathematical Society