Abstract
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.
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Schedule a callMore From: Proceedings of the Royal Society of Edinburgh: Section A Mathematics
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