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Construction of solutions for compressible, isentropic Navier-Stokes equations in one space dimension with nonsmooth initial data

Published online by Cambridge University Press:  14 November 2011

David Hoff
David Hoff
Affiliation:
Department of Mathematics, Indiana University, Swain Hall East, Bloomington, Indiana 47405, U.S.A.
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Extract

We prove the global existence of weak solutions for the Cauchy problem for the Navier-Stokes equations for one-dimensional, isentropic flow when the initial velocity is in L2 and the initial density is in L2 ∩ BV. Solutions are obtained as limits of approximations obtained by building heuristic jump conditions into a semi-discrete difference scheme. This allows for a rather simple analysis in which pointwise control is achieved through piecewise H1 and total variation estimates.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 103 , Issue 3-4 , 1986 , pp. 301 - 315
Copyright
Copyright © Royal Society of Edinburgh 1986

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References

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