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

Hoff, David; Zarnowski, Roger

Ann. Inst. Henri Poincaré, Anal. Non Linéaire 11, No. 2, 159-187 (1994).

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

Keywords:

discontinuous solutions of the Navier-Stokes equations; continuous dependence; rates of convergence; finite difference approximations

References:

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