Thats a tricky question.
Jesus said in Matt. 24:35 that Heaven and earth will pass away and Peter tells us in 2 Pet. 3:10-13 that the heavens will pass away with a great noise, and the elements will melt with fervent heat; both the earth and the works that are in it will be burned up.
Isaiah describes this event as well in many places. In Isaiah 13:13 he says that the earth will move out of her place, and in chapter 24 he says that God distorts its surface and that the earth fades away. Further in that chapter he says that the foundations of the earth will be shaken and will be violently broken. It will be split open and shaken exceedingly. It will reel to and fro like a drunkard and will totter like a hut. Isaiah goes so far as to say that the earth will fall, never to rise again.
Then in Isaiah 65 He tells us that God will create new heavens and a new earth.
The TRICKY part is that in Psalms it says that the earth is established forever and will not be moved forever.
Ps. 104:5:You who laid the foundations of the earth,
So that it should not be moved forever,
Ps. 78:69: And He built His sanctuary like the heights,
Like the earth which He has established forever.
And Eccl. 1:4:One generation passes away, and another generation comes; But the earth abides forever.
So I guess I would have to say that the earth AS WE KNOW IT will most definitely not remain forever. But God will create everything new!