Do Sunnis believe in the Mahdi, and who is he according to them?

The Sunnis believe that the awaited Mahdi will appear at the end of time and rule for seven years, during which he will fill the earth with justice. The Prophetic Sunnah has clarified his name, description, and place of emergence. He is from the household of the Prophet (peace and blessings be upon him), from the descendants of Fatimah. His name will match the Prophet's name, and his father's name will match the Prophet's father's name. He will have a broad forehead and a prominent nose, and Allah will rectify him in a single night. He will emerge from the East and be pledged allegiance to at the Kaaba after a conflict between three sons of caliphs, and black banners will emerge for him. A sign of his leadership is that Jesus, son of Mary (peace be upon him), will pray behind him when he descends. The number of hadiths concerning the Mahdi has reached the level of tawatur ma'nawi (connotative unbroken transmission), and belief in his emergence is obligatory. As for the hadith, "There is no Mahdi except Jesus son of Mary," it is weak.