After judgement day the wrongdoers go to hell and the ones who pleased Allah go to heaven, but what will happen with the earth?
Everything will be destroyed at the judgement day, everyone is revived from the death.
As Allah says in surat Al Qariah:
and in surah Altakwir:
At the judgment day and before just after the Horn is blown everything in Earth will be destroyed and flushed, and there is plenty of Ayat talking about that. Indeed The last part(Juzeh) all of it talks about that day.
Some of the states that ALLAH talk about:
and many other Surat and Ayat talks about that day.
But back to your question. You ask what happen after that day...
Will the Earth be part of the heaven or part of the hell!!! this is the point to talk about.
Some says that it will be a part of the Heaven and they prove with the Aya
And they claim that the heaven is already founded but is unseen by us.
While others say this Aya is just an example to show how wide will be and it doesn't indicate the real state of Earth.
So this is just explanations and nobody really knows what will it be after the judgment day
Muhammad Ibn Muslim narated from Imam Baqir a.s.:
According to this hadith a new earth with new kind of humans will be created and they will worship God.