I think Putin knows he is fucked.

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8. I don't think this is true at all.

I agree that taking over the whole of Ukraine is proving much harder than he expected. He may yet succeed, though the sanctions would stay if he did that.

However, all his pre-invasion propaganda was only about the two eastern regions of Ukraine. So he really doesn't lose much face at all if he gives up on the rest of Ukraine (for the time being) as long as he gets "something" regarding those two eastern regions.

One possibility is that once he has solid control of those regions (much easier to achieve than the whole of Ukraine), he agrees to withdraw from the rest of Ukraine in exchange for those two regions, or did making those two regions independent from both Russia and Ukraine, an arrangement where he could easily enough control thing anyway.

Hopefully Ukraine and its allies don't agree to this, but when peace and normal business is back on the table, Ukraine might not have enough support to keep fighting for just those two regions.

Point is, he doesn't have to conquer all of Ukraine to still have a face-saving path out of this.