# Bounds for the Vector Amplitudes

# Bounds for the Vector Amplitudes

This chapter estimates the bounds for the vector amplitudes *v*subscript *I* and *w*subscript *I* of the correction. It first presents the proposition about deriving the estimates for the transport part of *v*subscript *I* and proceeds by computing estimates for *v*subscript *I*, starting with the spatial derivatives. It then introduces a second proposition dealing with spatial derivatives of vector amplitudes and a third proposition for the first material derivative of vector amplitudes. The fourth proposition is concerned with the second material derivative of the vector amplitudes. The chapter shows that all the bounds for γsubscript *I* and αsubscript *I* are identical until the second material derivative. It concludes with a corollary about estimates for corrected amplitudes.

*Keywords:*
vector amplitude, correction, transport, spatial derivative, first material derivative, second material derivative

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