I possess a lg 34" (the curved one), you can run it just fine with intel integrated graphics (my processor is a i7 4790k) if you don't use display heavy applications (like games).
You can also play very well with a dedicated graphic card and a gaming virtual machine (using vga passthrough and something like a gtx 980ti to run games well), in case you change your mind about gaming someday.
Biggest downside i found was that it was impossible for me to see my bios menu with this screen, i have no idea if this is grub related since i purchased the screen for my gaming vm, easily fix with a second screen which i use only for my fedora host.
Anyway, since you won't play, if you can find the reason of the issue i got and fix it you won't have any problem at all. You won't even need to install a specific driver.

2016-01-21 21:45 GMT+01:00 Wolfgang S. Rupprecht <wolfgang.rupprecht@gmail.com>:

Mark <mark2015@openmailbox.org> writes:
> One of my new year's resolutions is to upgrade the monitor on my Fedora
> 23 Desktop.
>
> I've been looking at a 34" curved 3440 x 1440 monitor. But first I want
> to make sure it actually makes sense to get such a large monitor for
> Linux and that there's a graphics card on the market that works well
> with Fedora and that can drive such a large monitor. I would prefer an
> open source driver, but I'm prepared to install a blob if I have to.
> I'm not interested in gaming so that's not an issue, it's the real
> estate I'm after. 

Have a look at the ASUS R7360-OC-2GD5 or the same ATI/Radeon R7-360 card
by any of a half dozen companies.  I have one attached to a cheap 4k
Seiki HDMI monitor (8M pixels) which is 3M pixels more than you need to shift
(5M pixels).  Xorg works with it out of the box.  No mystery binaries
needed.

The downside is this card has a fan, but it runs very slowly under Xorg
and normal use.  Modern framebuffers just don't come fanless any more.
The GPU's at idle all seem to use just a touch too much power.

-wolfgang
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