Gaussian blur pixelation

As long as you work in 16 bit color depth, any banding you see is in your display system.

Even if the file is 16 bit, your display pipeline is 8 bit (unless you have an expensive 10-bit capable monitor). That's where the banding happens.

It's not in the underlying data. If it bothers you, a little noise will break it up, as Semaphoric describes.

First off, this may not be in the data, it may be simply part of the display path. You first must always view this at 100% zoom or greater. Zooming OUT subsamples the preview and isn't an accurate way to view the data.

Even in 16-bit, if your display path isn't fully high bit (more than 8-bits per color), meaning the video card and display itself, you can still see banding. Again, this isn't in your data, it's a result of the bit depth of the video path.

So there may be an issue here or maybe, it's how you're viewing the data. We need more info to know.

Work in 16bit. 

Did you apply the Filters as Smart Filters? 

As you saw, blurring makes it look worse. A common way of dealing with this is to add a small amount of noise to the area with banding, just enough to obscure the banding, but not so much to make it look "noisy" (less than 1%). If the problem area were a Smart Object, you could make changes to the amount of noise, while keeping your original intact.

Hi if you are applying a gaussian blur then this effect will be shown trying to save this as a jpeg and check it shows or not otherwise it depends your resolution of file try on 300...regards