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.


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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