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In order to emphasize the robustness of the tools that have been introduced hitherto in this book, we present in Chapter 6 a nonlinear system of partial differential equations with degenerate parabolicity. In fact, we show that some of the classical results for the Navier–Stokes system may be extended to the case where there is no vertical diffusion. Most of the results of this chapter are based on the use of an anisotropic Littlewood–Paley decomposition.
KeywordsGlobal Existence Energy Estimate Vertical Variable Stokes System Fourier Multiplier
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