I don't know how to open a .jp2 file.... I tried a while ago, and had given up.
On a mac, just double-clicking on the download will open it in Preview which is a weak freebie that comes with the operating system. From there you can adjust contrast fairly well, then take a screenshot (to greatly reduce file size, command-option-shift-4, and paste into your favorite photoshop-like software.
The problem comes if you want color. You can repeat the process on the visible bands to get RGB but it won't be possible to replicate the crop boundaries in Preview (as it doesn't support layer stacking). So then you would need to import into software like gimp that does and manually align the three channels and crop them simultaneously. Once the three grayscales are in register, any graphics software will display them as one natural color image.
It remains very perplexing why ESA chose an obscure format like jp2 (jeg2000) since it never gain any traction in the 15 years after it was proposed. At first I imagined that it offered some savings in file size (ie storage costs) for lossless compression.
The graphic below from polarview -- which unlike EarthExplorer offers you an opt-out -- suggest this is not the case -- there's no savings (though it needs a comparison with the standard format for 16-bit, namely tif).
My current theory is (1) they themselves use linux software that supports 16-bit jp2, (2) this being ESA's first venture into free imagery open to the public, they have no clue what public desktops can do, not knowing anyone themselves who uses AppleL or Microsoft products, (3) they made a dumb mistake but cannot admit it now because it would mean admitting to a dumb mistake plus creating a huge pipeline backlog, so (4) they'll continue with jp2 under the theory 'I got mine, fy.' That's the great thing about owning the satellite, you don't have to explain or justify anything, just do as you please.
As mentioned, wipneus is currently providing a 16-bit jp2-to-tif conversion service for Jakobshavn band 4 only. Try that site to see if the file sizes overwhelm your system. Most people can squeak by with the 8-bit files at the W/EB site or PolarView (which are not restricted to Jakobshavn).
I came across another unbelievable do-as-you-please change at DMI - an unsupervised graphic artist there decided to delete the Jakobshavn calving front from all the radar imagery! In favor of a white space, a big DMI promotional logo, and a repetitive locator map. Nothing can be done, even Danish registrants here never could get the time of day out of DMI.
i've worked on projects where enabling the biggest possible user community actually was a top priority. It all starts with working directly with typical users. If you let the programmers shield themselves behind multiple layers of help desk hires, feedback never happens.
After seeing the same thing on so many satellite server sites, I've come to realize there was never any sincere interest in opening access up to the unwashed public. So they just go through the motions, analogous to other social programs for non-whites.
https://drive.google.com/folderview?id=0B8NUHa4P2gmlfnhfcUwtRHVzZmRnWnZhQ0UwSkI3ZW12R0dYQ0R4UUR5eElPeEJSYzBsRFk&usp=sharing#list