I have no idea if it is country specific, but in our country if someone doesn't know something he or she would put their lower lip forward.
However, I cannot find a name for this lip gesture. Any help is appreciated.
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The Gallic shrug includes both the moue (facial gesture) along with the shoulder shrug
"Raise your shoulders; hold up your hands, palms out; stick out your lower lip; raise your eyebrows;"
The word for this gesture is pout. In the US and other anglophone nations, pouting usually indicates annoyance or exasperation. So, I wouldn't call this the "I-don't-know" gesture (words like shrug, etc, come to mind for this), but pout is the word you are looking for here.
pout: push one’s lips or one’s bottom lip forward as an expression of petulant annoyance or in order to make oneself look sexually attractive NOAD
to pout: may come close to what you are looking for:
To protrude the lips in an expression of displeasure or sulkiness.
To project or protrude.