# Bounds for Coefficients from the Stress Equation

# Bounds for Coefficients from the Stress Equation

This chapter estimates the bounds for coefficients from the Stress equation. It starts by considering the coefficients γsubscript *I* and the equation that implicitly defines it. It then estimates the derivatives of γsubscript *I* by differentiating the equation. The first transport derivative always costs a factor Ξ*e*ᵥ½ in the estimates, and each spatial derivative costs a factor of Ξ until the total order of differentiation exceeds *L*, at which point one obtains a larger cost of *N*superscript 1/*L*Ξ per derivative. The chapter also considers the bounds satisfied by the coefficients γsubscript *I* and shows that the final bound for the coefficients γsubscript *I* is exactly the same quality as the corresponding bound for ε.

*Keywords:*
coefficient, Stress equation, transport derivative, spatial derivative

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