There are a number of passages in the Bible which state unequivocally that the earth, in some form, is going to continue eternally. "One generation passeth away, and another generation cometh: but the earth abideth for ever" (Ecclesiastes 1:4).
However, this present earth and its atmospheric heavens must first be purged of all the age-long effects of sin and the curse, which now affect the very elements (or "dust of the earth"). Therefore, "the heavens shall pass away with a great noise, and the elements shall melt with fervent heat, the earth also and the works that are therein shall be burned up" (2 Peter 3:10).
Evidently, this fiery cataclysm is not an annihilation of the earth and its atmosphere, but rather a great exchange of energies. The earth's very elements will probably be converted into sound and heat energies by mass-energy nuclear-conversion processes, in order to burn out the great fossil beds and all other relics of sin and the curse. Then, however, God will reverse the process, converting these and other energies back into matter, thus "renewing" the primeval earth, which originally had been "very good" (Genesis 1:31). "We, according to his promise, look for new heavens and a new earth, wherein dwelleth righteousness" (2 Peter 3:13).
It is this new earth (that is, the earth made new) which will then continue forever. "For as the new heavens and the new earth, which I will make, shall remain before me, saith the LORD, so shall your seed and your name remain" (Isaiah 66:22). "Because the |creation| itself also shall be delivered from the bondage of corruption into the glorious liberty of the children of God" (Romans 8:21). Then we shall forever "be with the Lord" (1 Thessalonians 4:17). HMM