Will Jesus reign on David's earthly throne in Jerusalem?
Yes. Scripture teaches Jesus will reign on David's earthly throne in Jerusalem. David's throne was on earth, not in heaven. The prophet says His government and peace will have no end upon that throne, established with judgment and justice by the zeal of the Lord of hosts.
Les explains from Isaiah that the Son given to the nation of Israel will set up His kingdom, and of His government and peace there shall be no end, not from heaven but from the throne of David. He asks where David's throne was and answers that it was on earth, and says that is the same throne Jesus is going to assume in Jerusalem. The kingdom is ordered and established with judgment, rule, and justice, and the zeal of the Lord of hosts will perform it.
Of the increase of his government and peace there shall be no end, upon the throne of David, and upon his kingdom, to order it, and to establish it with judgment and with justice from henceforth even for ever. The zeal of the LORD of hosts will perform this.