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

Hoff, David

doi:10.1090/S0002-9947-1987-0896014-6

Global existence for $1$D, compressible, isentropic Navier-Stokes equations with large initial data
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Trans. Amer. Math. Soc. 303 (1987), 169-181 Request permission

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

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