We establish a minimal positive existence time of the parametric Willmore flow for any smooth initial data (smooth immersion of a closed oriented surface). The minimal existence time is a function exclusively of geometric data which in particular are all well defined for general weak Lipschitz <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mi>W</m:mi> <m:mrow> <m:mn>2</m:mn> <m:mo>,</m:mo> <m:mn>2</m:mn> </m:mrow> </m:msup> </m:math> W2,2 immersions. This fact opens in particular the possibility for defining the Willmore flow for weak Lipschitz <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mi>W</m:mi> <m:mrow> <m:mn>2</m:mn> <m:mo>,</m:mo> <m:mn>2</m:mn> </m:mrow> </m:msup> </m:math> W2,2 initial data.
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Palmurella et al. (2024) studied this question.