Isaiah 54:7-10

For a brief moment I deserted you,
    but with great compassion I will gather you.
In overflowing anger for a moment
    I hid my face from you,
but with everlasting love I will have compassion on you,”
    says the Lord, your Redeemer.

“This is like the days of Noah to me:
    as I swore that the waters of Noah
    should no more go over the earth,
so I have sworn that I will not be angry with you,
    and will not rebuke you.
For the mountains may depart
    and the hills be removed,
but my steadfast love shall not depart from you,
    and my covenant of peace shall not be removed,”
    says the Lord, who has compassion on you.

Hebrews 9:11-15

But when Christ appeared as a high priest of the good things that have come, then through the greater and more perfect tent (not made with hands, that is, not of this creation) he entered once for all into the holy places, not by means of the blood of goats and calves but by means of his own blood, thus securing an eternal redemption. For if the blood of goats and bulls, and the sprinkling of defiled persons with the ashes of a heifer, sanctify for the purification of the flesh, how much more will the blood of Christ, who through the eternal Spirit offered himself without blemish to God, purify our conscience from dead works to serve the living God.

Therefore he is the mediator of a new covenant, so that those who are called may receive the promised eternal inheritance, since a death has occurred that redeems them from the transgressions committed under the first covenant.

Question: Why does the world continue after judgment?

Answer:  Because God, in grace, has covenanted to preserve creation for the sake of redemption in Christ.

Genesis 9:16
“When the bow is in the clouds, I will see it and remember the everlasting covenant between God and every living creature of all flesh that is on the earth.”