First of all, the AMD Radeon HD 7970 graphics card is a 28nm beast that boasts 2048 Stream processors, 128 texture units, 925MHz core clock, 3GB of 5.5GHz effective GDDR5 memory on a 384-bit bus, and is their first product of GCN (Graphics Core Next), their new graphics architecture. The launch cost on her is $549 USD. GCN represents the largest architectural change for AMD since they launched the R600 GPU several years ago.
So how does the Radeon HD 7970 "Tahiti" work under Linux? Well, you can have OpenGL and compute support right now under Linux with the HD 7970 should you be using the latest AMD Catalyst Linux driver. The support is in place just like the Windows driver and is available at-launch as AMD has been doing for Linux since the Radeon HD 4800 "RV770" series a few years ago.
The open-source driver support is not yet available. No patches have magically landed this morning and they haven't released any support work in advance of the hardware's availability. The open-source Radeon HD 7000 series support will require significant driver changes to the Radeon DRM kernel component as well as a brand new Gallium3D driver, which is being based upon a stripped-down version of R600g.
Even when all of the initial support pieces are in place, you will still be in an OpenGL ~2.1 world with limited performance, so if you have just spent over $500 USD on a high-performance Radeon HD 7970 chances are you will not want to use the open-source Linux driver anytime soon. You'll also be without OpenCL/Compute support initially, unless using the AMD binary blob driver.
For full details about the Radeon HD 7000 series Linux driver support, read: Radeon HD 7000 Series Linux Driver Support, AMD Driver Support State For Radeon HD 7000 Series, and Radeon HD 7000 Series Will Bring New 3D Driver.
As far as how well the Radeon HD 7970 is working under Linux with the Catalyst driver, that is a good question. AMD decided not to send out any HD 7970 sample to Phoronix in advance, so as such, there is no Linux information available to the public this morning with benchmark results or other information. I don't know if they will decide to send one in the next few days or not, but hopefully, so then I don't have to spend $549 USD on the graphics card or just let Linux enthusiasts go in the dark about HD 7970 information. It's a same though especially when they're users of the Phoronix Test Suite, etc. [At least though they're sending out a new APU and that will be here tomorrow so I can be occupied with some new AMD APU Linux tests on Christmas.]
If you would like to see any Windows reviews of the new AMD Radeon HD 7970 3GB PCI Express graphics card, there are a number of Radeon HD 7970 reviews that were found automatically this morning by the OpenBenchmarking.org engine. Stay tuned (and follow me on Twitter) for more information as soon as I manage to get my hands on an AMD Radeon HD 7970, GCN and the graphics card itself look quite nice.