The assault on Fallujah (Operation Al-Fajr [“Dawn”]/Phantom Fury) continues today. Today’s New York Times has a very useful map (another good one can be found at GlobalSecurity.org). From the New York Times article, the main effort is east of the Euphrates, on the north side of the city. On the NYT's map, six US battalions are advancing on a front of just under four miles. The line-up (from east "left" to west "right") is: 2/2nd US Inf., 1/3rd Marines, 1/8th Marines, 2/7th Cavalry, 3/5th Marines, 3/1st Marines. That’s a tremendous amount of force on a narrow front.
The two marine battalions on the right (3/5, and 3/1), are assaulting the Jolan District, which is supposed to be the rebels' main stronghold, and which seems to be the roughest sector. Orbat.com says that the left wing of the advance (opposite the Askiri District of the city, in the north east), is “halfway or more to the center of the district."
According to Orbat.com, to the west of the city, 36th Commando Battalion, Iraq National Guard, corseted with US Marines, seized the main hospital and two of the Euphrates bridges yesterday. An unidentified Marine unit may have crossed the Euphrates. Unidentified Iraqi government units (no doubt backed by US formations) have attacked in the southeastern part of the city.
Orbat says that British units are helping blockade the city west of the Euphrates, but this is questionable, the New York Times puts the Black Watch Battle Group (the main concentration of British troops in the area), nearer Baghdad. Other US and Iraqi forces seem to be operating to the east and south, blockading the city from those directions as well.
Predictable criticism is beginning to be heard from the usual suspects, mostly the UN and its associated organizations, and the Russians. Hopefully, the government ignores this and finishes with the Fallujah rebels.