Abstract
In this section we introduce the Nash inequality and its generalized version, the Gagliardo–Nirenberg inequality. Roughly speaking, these inequalities provide estimates for an integral of a function by its derivatives, a tool that is very helpful not only in the analysis of the vorticity equations as demonstrated in Chapter 2, but in the analysis of nonlinear PDE in general.
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Giga, MH., Giga, Y., Saal, J. (2010). Calculus Inequalities. In: Nonlinear Partial Differential Equations. Progress in Nonlinear Differential Equations and Their Applications, vol 79. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4651-6_6
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DOI: https://doi.org/10.1007/978-0-8176-4651-6_6
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Publisher Name: Birkhäuser Boston
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Online ISBN: 978-0-8176-4651-6
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