[Goose]

I wonder if the short term logistical situation is partially mitigated by local supplies. These Russian towns have cars, gas, food, water, etc that can be used to fuel further advances.

Indeed that will help for awhile. Food and water are bulky, so anything the troops can obtain locally will be useful. Getting reliable and clean fuel would be nice but historically attempts to "live off the land" that way haven't worked. Too easy for retreating Russian troops to render the fuel unusable or just set it on fire. Civilians can do the same if they want to  :-).

The problem will be ammunition (particularly artillery ammunition) and replacements. Both will be required in pretty large quantities. Ukraine also has had no time to really fortify any of the towns they occupy. The force being used is a mobile combined arms grouping, supposedly. Such forces require lots of logistics.

You also have to wonder how Russia will respond when trying to retake territory. Their only effective method has been to flatten settlements with artillery and glide bombs. Are they willing to do that with Russian towns, some of which will still have civilians within them?

Indeed, but these Ukrainian towns were fortified pretty well by Ukrainian troops that intended to defend there. They know the area well, which also helps. That will not be true inside Russia, especially in so far as the offensive is a mobile striking force. Such a force doesn't want to EVER stop and defend. Much of its combat effectiveness is derived from striking unprepared (and hopefully inadequate and disorganized) enemy formations who also have had no time to fortify and "dig in" their defenses. The "follow up" forces are the ones who will fortify and defend. Does Ukraine have a "follow-up" force ready to do this and if so, how big?

Assuming Ukraine does intend to defend a lot of what it has recently taken, has time to dig in/fortify, and has enough troops, Russia will indeed have the dilemma you describe. IMO the Russians will try to cut Ukrainian communications, not slug it out in a destructive "Stalingrad" battle. That is what a "sane" Russian would do. Get the VVS off their dead ass and bomb Ukrainian communications to the point Ukraine has to pull back. This fight will be inside Russia, so Ukraine will only have whatever air defense assets it could bring to the area. It will be interesting to see what Russia does if things play out this way.

[Goose]

I wonder if the short term logistical situation is partially mitigated by local supplies. These Russian towns have cars, gas, food, water, etc that can be used to fuel further advances.

Indeed that will help for awhile. Food and water are bulky, so anything the troops can obtain locally will be useful. Getting reliable and clean fuel would be nice but historically attempts to "live off the land" that way haven't worked. Too easy for retreating Russian troops to render the fuel unusable or just set it on fire. Civilians can do the same if they want to  :-).

The problem will be ammunition (particularly artillery ammunition) and replacements. Both will be required in pretty large quantities. Ukraine also has had no time to really fortify any of the towns they occupy. The force being used is a mobile combined arms grouping, supposedly. Such forces require lots of logistics.

You also have to wonder how Russia will respond when trying to retake territory. Their only effective method has been to flatten settlements with artillery and glide bombs. Are they willing to do that with Russian towns, some of which will still have civilians within them?

Indeed, but these Ukrainian towns were fortified pretty well by Ukrainian troops that intended to defend there. They know the area well, which also helps. That will not be true inside Russia, especially in so far as the offensive is a mobile striking force. Such a force doesn't want to EVER stop and defend. Much of its combat effectiveness is derived from striking unprepared (and hopefully inadequate and disorganized) enemy formations who also have had no time to fortify and "dig in" their defenses. The "follow up" forces are the ones who will fortify and defend. Does Ukraine have a "follow-up" force ready to do this and if so, how big?

Assuming Ukraine does intend to defend a lot of what it has recently taken, has time to dig in/fortify, and has enough troops, Russia will indeed have the dilemma you describe. IMO the Russians will try to cut Ukrainian communications, not slug it out in a destructive "Stalingrad" battle. That is what a "sane" Russian would do. Get the VVS off their dead ass and bomb Ukrainian communications to the point Ukraine has to pull back. This fight will be inside Russia, so Ukraine will only have whatever air defense assets it could bring to the area. It will be interesting to see what Russia does if things play out this way.