It is gathered from the evidences and proofs in the verses of the Quran that the Day of Judgment is in fact not the continuation of this world. This world shall turn into a mess completely because great explosions and horrific quakes will destroy everything. Thereupon, the world will emerge with a new design on the mess and ruins of this world. According to the same evidences, the resurrection of human beings shall take place in that new world.
Nonetheless, it has been reported in the traditions that God, the Almighty, will create a new world after the destruction of this world and following the Day of Judgment when the people of Paradise will settle in Paradise and the People of Hell in Hell. Then, God shall create a world which will be different from the present world and creatures.
An answer to this question depends squarely on an appropriate understanding of the Day of Judgment, resurrection and its signs. We will therefore elaborate on some of the signs of the Day of Judgment and then an answer will follow to the foregoing question:
First: What is inferred from the verses of the Holy Quran is that the world ends with the arrival of the Day of Judgment and that a new world will come into being after the day of Resurrection. The Holy Quran has made mention of some signs which we shall mention under three categories:
A) Incidents which take place before the end of the world: One of the pre-resurrection signs is the coming of the last Messenger. Another sign of the end of this period is a smoke that will appear in the sky. The Quran says: "Then watch thou for the Day that the sky will bring forth a kind of smoke (or mist) plainly visible."
It is narrated that a companion of the Holy Prophet (s) asked him, “What is this smoke?” The Holy Prophet (s) recited the above verse and then said, “This is such a smoke that will envelope the entire world from east to west, and it will remain for 40 days and 40 nights. A believer will experience the uneasiness of cold (like hay fever), whereas the smoke will come out of the nose, ears and rear of a disbeliever”.
B) Incidents which take place on the verge of the end of the world:
1. The mountains will be crushed following a few other incidents. They will be shaken by quakes, lifted up and then they will be moved and crushed at one stroke. Then they will turn into a heap of sands and then they turn into dust and disperse.
3. Devastating quakes: On the Day of Judgment, an ear-shattering sound will follow the sounding of the trumpet, and an unequalled tremor will rock Earth. Massive mountains, trees—in fact every place on Earth—will begin to rock at the same time. People will panic and be gripped by great fear. The most fear-inspiring aspect is that no one can escape it or find any sort of refuge, for this tremor is not like the ones with which we are familiar; rather, this tremor will continue until Earth has been flattened: "Mankind, heed your Lord! The quaking of the Hour is a terrible thing."
4. On the Day of Judgment, the Sun and the Moon, the Earth's two sources of light, will be darkened one after the other: "When the sun (with its spacious light) is folded up; When the stars fall, losing their luster."
5. The sky and other planets are rent asunder: "When the heaven is split asunder."
6. The incidents which will be created at the start of the Day of Judgment and resurrection:
The last stage of the Judgment Day involve incidents which take place following the two preceding stages: " On the day when the earth shall be changed into a different earth, and the heavens (as well), and they shall come forth before Allah, the One, the Supreme.", 
It can be concluded from the above that the Day of Judgment is not the continuation of this world. This world shall turn into a mess completely because great explosions and horrific quakes will destroy everything. Thereupon, the world will emerge with a new design on the mess and ruins of this world. The resurrection of human beings shall take place in that new world.
Second: There are also other evidences in the Quran which somehow substantiate the temporariness of this world. For example, the Holy Quran says, "We created not the heavens and the earth and all between them but for just ends, and for a Term Appointed." That appointed day or term is the Day of Judgment when the skies and the earth are folded up and the earth will go through a metamorphic change. Not only the earth but also the sun, moon and other planets will not be in this system for ever. Their movement and the system in which they operate are for a temporary period of time. When the appointed time expires, then they will be overthrown and rent asunder.
Scientific predictions made about the world and the existing system also accord, to a great extent, with the revelation and religious underpinnings. If there is a view opposing the revelation, it is, according to us, nothing but a conjecture which is soon or late perfected or modified by other scholars and drawn closer and nearer to the realities of the Quran.
Third: As for whether or not God will create a new creature following the Day of Resurrection and upon people's going to Paradise and Hell, it is a question which has been touched by some traditions:
Jabir bin Yazeed says that he asked Imam Baqir, peace be upon him, about this verse: "Were We then worn out by the first creation? Yet they are in doubt about a new creation. "
He (Imam Baqir) said, “O Jabir, the explanation of that verse is that when Allah, the Exalted, will destroy this creation and this world, and doom people to living in paradise and in hell then Allah, the Sublime, will create a new cosmos from the beginning, and will create a new creature without male or female that will worship Him and accept the oneness of Him. Further, He will create a new earth without this earth for that creature, which will carry the burden of it. And He will create a new sky/heaven other than this sky that will spread its shadow on them.
Perhaps you think God has created only one universe and you think God has not created any man except you.
Yes by Allah, the Sublime, who has created thousands of universes and thousands of Adams, you are in the last of the worlds and you are the last descendants of those Adams"
Late Allamah Muhammad Hussein Tabatabai (may his soul rest in peace) quote this meaning and considers it as one of the possible (not the only) meanings of this verse.
Therefore, this world with its sky and earth will be overthrown after the Day of Judgment. And if a world is also created, it will have different features and would be beyond our imagination and perception.
For further information, see the following indexes:
1. The Nature of the Relationship of Action with Temporal Incidents, question 2229 (site: 2525)
2. The Age of Mankind, 637 (site: 701).
3. The creation of Adam and the Findings of Scientists, 2999 (site: 3297)
 - Makarem Shirazi, Naser, Payam-e Qur'an (The Message of the Quran), vol.6, pg. 21, Amirul Momeneen School Publications, 1374 (1995).
 -Dukhan, 10
 - Payam-e Qur'an (The Message of the Quran), vol.6, pg. 27, Amirul Momeneen School Publications, 1374 (1995)
 -Al-Muzzammil, 14
 - Al-Haqqah, 14
 - Tur, 10
 - Al-Haqqah, 14
 - Al-Muzzammil, 14
 - Al-Waqeah, 5 and 6.
 - Al-Infitar, 3
 - Al-Takwir, 6.
 - Al-Hajj, 1.
 - Al-Takwir, 1 & 2.
 - Al-Inshiqaq, 1.
 - Ibrahim, 48
 - See: question 1946 on our website.
 - Makarem Shirazi, Naser, Payam-e Qur'an (The Message of the Quran), vol.6, pg. 40
 - Al-Ahqaf, 3.
 - Qira'ati, Mohsen, Resurrection, pg. 200, Jame'ah Islamic Modarresin Publications, Qom, 3rd edition.
 - Ibid, pg. 201.
 - Quran, Qaf 50, 15 أَ فَعَیِینا بِالْخَلْقِ الْأَوَّلِ بَلْ هُمْ فِی لَبْسٍ مِنْ خَلْقٍ جَدِیدٍ"
 - Faiz Kashani, Tafsir al-Saafir, vol.5, pg. 60, Tehran, Sadr, 1415 A.H.
 - Tabatabai, Muhammad Hussein, translation by Muhammad Baqir Musavi Hamedani, vol.18, pg. 534, Jame'ah Modarresin Publications, Qom, 1374 (1995).