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The U.S. has been bombing the Islamic State for two months now, and several developments stand out: The extremists are still on the offensive, the U.S. is struggling to find partners on the ground, and for the first time in a quarter-century, a major U.S. military intervention lacks a formal name.

When President Obama launched the aerial campaign in August against the so-called Islamic State in Iraq, followed a month later with similar strikes in Syria, it carried the expectation that it could grind on for years.

Still, the slow start stands in contrast to the U.S. military actions that rapidly toppled, or helped topple, governments in Iraq, Afghanistan and Libya since 2001.

The Battle On Turkey's Border

If the Islamic State — aka ISIS and ISIL — was supposed to retreat in the face of the U.S. air campaign, it apparently didn't get the memo.

As NPR's Tom Bowman notes, U.S. and coalition forces have carried out nearly 400 airstrikes in Iraq and Syria. But locating targets is growing more difficult. Islamic State fighters are moving into mosques and schools in the cities. They are avoiding travel on open desert roads and are turning off cellphones and radios so they can't be pinpointed.

While Islamic State fighters have been pushed back in a few areas, this week's fighting has focused on their offensive in Kobani, a mostly Kurdish town on Syria's northern border with Turkey. Turks can literally watch the fighting from their side, and the smoke rising from Kobani occasionally wafts across the frontier.

(The U.S. is bombing from the skies, and Kurdish fighters have been battling the Islamic State on the ground, but that may not be enough to keep the extremists from taking control of a city that sits on the border. The militants now control one-third of the strategic border town, according to the Britain-based Syrian Observatory for Human Rights.)

The Islamic State has also made gains in the past couple of weeks in western Iraq, while the Iraqi army has yet to show any signs that it can confront and push back the extremists.

The one bright spot so far is northern Iraq, where Iraqi Kurdish fighters took a string of towns near the Syrian border last week, building on earlier gains over the past two months. However, Mosul, the largest city in northern Iraq, remains firmly under the control of the Islamic State.

A Coalition Still In Flux

The U.S. boasts more than 40 countries in its coalition, including five Arab monarchies that are taking part in the air operations. But the fighting in Kobani illustrates the limits of that cooperation so far.

The U.S., Turkey and the Kurds throughout the region are all opposed to the Islamic State. But they all have their own agendas and haven't been able to coordinate their goals, let alone their actions.

Kurds from Syria and Turkey have been fighting back against the Islamic State in Kobani, but may not be strong enough to hold them off. The U.S. is bombing the Islamic State fighters, but there's no indication that the Americans are coordinating directly with the Kurds.

One reason for the lack of coordination is that Turkey and the U.S. regard at least some of these Kurdish fighters as belonging to terrorist groups.

This has created the odd situation where Turkey, a NATO member, has the Islamic State fighting on its border and has not intervened. Turkey has positioned tanks near the frontier, but they have yet to fire any shots.

The Turkish security forces are in action, however, against Kurdish protesters inside Turkey. More than a dozen protesters were killed Tuesday as they demonstrated against the Turkish government for its policies toward the war in Syria.

NPR's Peter Kenyon reported that "Kurds have been basically told by their leaders to go help the Syrian Kurds across in Kobani who are fighting ISIS, but the Turkish border guards aren't letting them go.

"Kobani is so close to the border that people can literally watch it begin to fall. They can't do anything to help, and the anger after these deaths, especially, is only likely to grow," he told Morning Edition.

Meanwhile, the moderate Free Syria Army, which the U.S. is seeking to bolster, is nowhere to be found in this particular fight.

Operation Fill-In-The-Blank

The Pentagon has named every U.S. military intervention from the Panama invasion in 1989 (Operation Just Cause) to the current effort to contain the Ebola outbreak in West Africa (Operation United Assistance).

Yet the bombing campaign in Iraq and Syria has yet to receive a moniker, which to critics is emblematic of its fuzzy nature.

Pentagon Press Secretary Rear Adm. John Kirby said last week there is "an effort under way to consider ... a potential name for this operation."

This may sound like a minor bureaucratic matter, but it does affect issues such as assigning costs in the military budget and the awarding of medals.

There's also the question of whether this battle against the Islamic State is formally defined as a war or, as the Obama administration would prefer, a counterterrorism operation. It's a distinction that matters, according to Karen DeYoung in The Washington Post.

"It matters to the American people, who have said in surveys that they favor airstrikes against Islamic State militants in both Syria and Iraq but aren't much interested in fighting another Middle East ground war," she says. "It also matters to Congress, which has not authorized a war since World War II but may decide to approve this specific 'use of military force.' "

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