PDF reader on Linux capable of continuous updating

Evince and Okular will auto-reload when the file being viewed changes. So does another option: Zathura.

That said, my recommendation would still be MuPDF instead, though it'll take some more work to set up. The reason is that MuPDF in general is a much faster program, and will reload faster. It doesn't auto reload like these do, but this can be solved.

I don't use latexmk personally, but if memory serves, there's a way of make it call a certain command at the end of a successful command. You can set it up to send MuPDF the SIGHUP signal, which refreshes it. I did something similar for a vim live latex plugin I wrote years ago, which I abandoned. However, it was forked and exists here on GitHub.

Here's it is in action:

(EDIT: I don't use this anymore, so I changed the links above to a clone of it made by someone else on GitHub.)

The most commonly used are Evince and Okular (whether you are respectively using GNOME/XFCE or KDE).

You can get automatic updating with xpdf by setting the following in ~/.latexmkrc:

$pdf_previewer = "start xpdf -remote %R %O %S";
$pdf_update_method = 4;
$pdf_update_command = "xpdf -remote %R -reload";

These settings are straight out of the latexmk documentation. I've found this works very well, and is my preferred solution at the moment. It has the advantage that xpdf doesn't update its screen until told to do so by latexmk, which is after it has finished making the pdf file.

(I used to use gv -watch, but, particularly with big files, gv regularly tried to do a screen update before the viewed file was completely made, which resulted in a mess.)