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Continuous dependence in \(L^ 2\) for discontinuous solutions of the viscous \(p\)-system. (English) Zbl 0836.35157

Summary: We prove that discontinuous solutions of the Navier-Stokes equations for isentropic or isothermal flow depend continuously on their initial data in \(L^2\). This improves earlier results in which continuous dependence was known only in a much stronger norm, a norm inappropriately strong for the physical model. We also apply our continuous dependence theory to obtain improved rates of convergence for certain finite difference approximations.

MSC:

35R05 PDEs with low regular coefficients and/or low regular data
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35Q30 Navier-Stokes equations
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
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References:

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