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.
KeywordsHeat Equation Bounded Linear Operator Sobolev Inequality Singular Integral Operator Lorentz Space
Unable to display preview. Download preview PDF.