The United States, along with its foreign partners, launched its airstrikes in Syria against the Islamic State on Monday.

“This is the punch in the nose to the bully that we talked about on the playground,” former Delta Force officer James Reese told CNN. “ISIS is the bully, and we just punched him in the nose.”

According to U.S. military officials, the purpose of the airstrikes is to hinder and break down the Islamic State’s ability to command, control, resupply, and train.

Joined by five other Arab states in the airstrikes, President Obama stated on Tuesday that “this is not America’s fight alone.” The Arab partners include Jordan, the United Arab Emirates (UAE), Bahrain, and Saudi Arabia.

“The overall effort will take time,” President Obama added. “There will be challenges ahead. But we are going to do what’s necessary to take the fight to this terrorist group.”

President Obama’s resolve against the Islamic State deepened with the militant group’s murders of American journalists in the past weeks, and the large numbers of Western members in the group. As a result, the U.S. has been seeing the Islamic State as not just a terrorist group, but a threat to American security. The country’s launch of airstrikes in Syria, however, has received ambivalent reactions internationally.

First, Syria has been claiming that the U.S. had notified them of the airstrikes in advance. The U.S. denied these allegations.

“We did not provide advance notification to the Syrians at a military level, or give any indication of our timing on specific targets,” Jen Psaki, spokeswoman for the State Department, told Wall Street Journal. She also denied the claim made by Syria that Secretary of State John Kerry had sent a letter to Walid al-Moallem, Syria’s Secretary of State.

However, this arbitrary attack by the U.S. without permission from the Syrian government, though the Syrian government claims it has been notified, has been criticized by Russia and Iran, according to the Wall Street Journal. They denounced the action as a violation of international law.

“Such actions must be carried out exclusively within the boundaries of international law,” said the foreign ministry of Russia. “That means not formal unilateral ‘notification’ of strikes but the clearly expressed approval of the government of Syria or the passage of a decision by the United Nations Security Council.

Wall Street Journal further reported that Hasan Rouhani, the president of Iran, agreed with Russia and condemned the U.S. airstrikes as illegal.

However, Army Lt. Gen. William Mayville Jr. told the Washington Post that amid the airstrikes, the Syrian forces “made no attempt to defend Syrian airspace.”

Most countries believe that the airstrikes are not sufficient to eliminate the threat of the Islamic State, according to the Washington Post.

“Contrary to the discourse in Washington, the Islamic State militants will not be defeated in airstrikes,” wrote a report from Le Monde, a French newspaper.

“The Islamic State is more of an idea,” Die Welt, a German media source, said. “One cannot just bomb the militants, but must fight them ideologically.”

The U.S. has not mentioned any other actions that it will take against the Islamic State other than airstrikes and an effort to help Iraq build a sustainable government. President Obama has mentioned repeatedly that the U.S. will not send ground troops to directly fight against the Islamic State.

Meanwhile, the U.S. military said that it’s too early to determine the effectiveness of the airstrikes. However, Rear Adm. John Kirby, the spokesman for the Pentagon, told Fox News, “We believe we hit, largely, everything we were aiming at.”