The Church certainly believes the Earth will be burned up; otherwise the Messianic hope which Christ has promised us cannot pass. Yet it will endure for ever, because the burning up of the Earth in the day of the Lord is not a destruction but a renewal; and all imperfect things will pass away and God's vision for His Creation will be made manifest.
From the Catechism:
671 Though already present in his Church, Christ's reign is nevertheless yet to be fulfilled "with power and great glory" by the King's return to earth.Lk 21:27; cf. Mt 25:31 This reign is still under attack by the evil powers, even though they have been defeated definitively by Christ's Passover.Cf. II Th 2:7 Until everything is subject to him, "until there be realized new heavens and a new earth in which justice dwells, the pilgrim Church, in her sacraments and institutions, which belong to this present age, carries the mark of this world which will pass, and she herself takes her place among the creatures which groan and travail yet and await the revelation of the sons of God."Lumen Gentium 48 #3; cf. II Pt 3:13; Rom 8:19-22; I Cor 15:28 That is why Christians pray, above all in the Eucharist, to hasten Christ's return by saying to him:Cf. I Cor 11:26; II Pt 3:11–12 Maranatha! "Our Lord, come!"I Cor 16:22; Rev 22:17,20
672 Before his Ascension Christ affirmed that the hour had not yet come for the glorious establishment of the messianic kingdom awaited by IsraelCf. Acts 1:6–7 which, according to the prophets, was to bring all men the definitive order of justice, love and peace.Cf. Is 11:1–9 According to the Lord, the present time is the time of the Spirit and of witness, but also a time still marked by "distress" and the trial of evil which does not spare the ChurchCf. Acts 1:8; I Cor 7:26; Eph 5:16; I Pt 4:17 and ushers in the struggles of the last days. It is a time of waiting and watching.Cf. Mt 25:1,13; Mk 13:33–37; I Jn 2:18, 4:3; I Tim 4:1
676 The Antichrist's deception already begins to take shape in the world every time the claim is made to realize within history that messianic hope which can only be realized beyond history through the eschatological judgement. the Church has rejected even modified forms of this falsification of the kingdom to come under the name of millenarianism,Cf. Dentzingen-Schönmetzer 3839 especially the "intrinsically perverse" political form of a secular messianism.Pius XI, Divini Redemptoris, condemning the "false mysticism" of this "counterfeit of the redemption of the lowly"; cf. Gaudium et Spes 20–21.
677 The Church will enter the glory of the kingdom only through this final Passover, when she will follow her Lord in his death and Resurrection.Cf. Rev 19:1–9. The kingdom will be fulfilled, then, not by a historic triumph of the Church through a progressive ascendancy, but only by God's victory over the final unleashing of evil, which will cause his Bride to come down from heaven.Cf. Rev 13:8; 20:7–10; 21:2–4 God's triumph over the revolt of evil will take the form of the Last Judgement after the final cosmic upheaval of this passing world.Cf. Rev 20:12, II Pt 3:12–13
Therefore, the Church believes that this world will be renewed, but that which is imperfect must pass away then (cf. I Cor 13:10). The Earth will endure forever, beyond its final purification in the Coming of the Lord.