Plus, Stephen Carter on why this is America's war, Daniel Stone asks if the intervention is legal, and full coverage of Libya.

Libya’s capital is under siege for the fourth night in a row, as a fresh round of Western aistrikes hit Tripoli again on Tuesday. “We’ve been hearing big noises. We’ve heard some explosions in the last 10 minutes,” said an Al Jazeera reporter in the city. Witnesses said the anti-aircraft strikes are zeroing in near the Gaddafi residence (his location is still unknown) and the capital’s air defenses are retaliating with fire. A ground battle continues to rage as well: Pro-Gaddafi troops reportedly killed dozens in the rebel stronghold of Benghazi today, defying the airstrikes.

Though Hillary Clinton begs to differ, Libyan leader Muammar Gaddafi insisted on Tuesday that he will overcome allied airstrikes against his nation, vowing in a brief speech that his forces “will be victorious in the end.” He also called on “all Islamic armies” to join him in his fight. As a dramatic background for his speech, Gaddafi spoke from Tripoli in front of the ruined façade of a site damaged by the U.S. airstrikes.

Photos: Intervention in Libya

Meanwhile, rifts are breaking out among the international coalition responsible for the strikes. The United States, facing a tepid popular reaction and anger from both the right and left over its involvement in the action, is pushing for a quick handover of the operation to NATO. But European leaders can’t come to terms on their reaction. France wants to lead the effort jointly with Britain, but the U.K., also gun-shy after the Iraq war, backs the NATO tack. German representatives stalked out of a meeting Tuesday, and everyone’s angry at French President Nicolas Sarkozy. With friends like these, who needs Gaddafi?