Thirteen Day War

From Gineipaedia, the Legend of Galactic Heroes wiki

The Thirteen Day war as a nuclear conflict fought on Earth in 2039 CE between the United States of Eurafrica and the Northern Condominium. Both states used Nuclear Weapons on each other, and were destroyed in less than two weeks. At the end of the war, all of Earth's major cities were destroyed and the human population had been reduced to a mere one billion.