Log-log convexity and backward uniqueness

Kukavica, Igor

doi:10.1090/S0002-9939-07-08991-5

Log-log convexity and backward uniqueness
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by Igor Kukavica

Proc. Amer. Math. Soc. 135 (2007), 2415-2421

DOI: https://doi.org/10.1090/S0002-9939-07-08991-5

Published electronically: March 14, 2007

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Abstract:

We study backward uniqueness properties for equations of the form \begin{equation*} u’ + A u = f. \end{equation*} Under mild regularity assumptions on $A$ and $f$, it is shown that $u(0)=0$ implies $u(t)=0$ for $t<0$. The argument is based on $\alpha$-log and log-log convexity. The results apply to mildly nonlinear parabolic equations and systems with rough coefficients and the 2D Navier-Stokes system.

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