You can use paging.

It means, in general terms, split your log file in numbered blocks (or sections). Each block has a given index.

For example, each block contains x rows. The JEditorPane contains one block at a time. The other blocks may persist in memory. When the JEditorPane-view reaches the beginning or end of each block you just exchange the current block with previous/next block.

This takes some programming, but can be done fairly easily.