I've decided to be a bit contrarian. Bear with me please. Even mozilla, and I am using Seamonkey which is the same interface as mozilla with Firefox-style coding, is a descendent of Netscape which in turn is a descendent of Mosaic. Why is that important? Because I learned Slackware on a college lab with X-Windows and Netscape installed after they installed it because they couldn't afford Unix. Got that? Linux is a kernel which was developed to run programs like the GNU Tools and X-Windows which were developed on UNIX and in the case of X-Windows can be widely seen on film and TV footage of University and NASA computers from the late eighties onward (under Bush Windows started replacing it -- there seems to have been a connection). Anyhow, Mosaic/Netscape/Mozilla/Seamonkey/Firefox was developed originally on X-Windows, not on Linux (on UNIX in fact as I recall). It did not need a substantial port over to Linux. It apparently just compiled the way everything else did. And it was ported over to Windows about six months later.
There is NO web browser available for Linux EXCEPT links I have not used some form of on UNIX and links is a descendent of lynx which I used when I last had a unix account. This is true of dillo, (try it on damn small linux), Opera, konqueror (yes there are KDE desktops on FreeBSD systems. Hey, Sun Solaris defaults to Gnome which means they have) Epiphany. You name it. The story goes this hotshot Sun Engineer was the head of a project. He was told at a meeting that his project was scheduled to be ported from Solaris to Linux. A little while later he showed up at the boss's office with an executable which ran. The amazed brass asked him how he'd done it, and he said, "Simple. I just typed 'make'."
Linux is a great prototyping environment because it strives to reproduce a generic Unix environment. When it develops or changes, everything becomes available to Unix -- and vice versa. Therefore no. There is no special browser for Linux. There are special browsers for posix-compatible (Unix and Unix-derived) Operating systems, and for the X-Windows desktop but by design Linux cannot have a monopoly because that's not what interests Linus Torvalds.
When you compare Linux to a proprietary operating system, you miss the point. There are so many programs available to *nix users which do things BETTER than Windows programs because their SOLE FOCUS is productivity, rather than productivity AND protecting owners rights. Some of them are venarable. I learned vi in 1989, about 10 years after Bill Joy wrote it at U Cal Berkely. Windows itself still seems to include a telnet.exe (even after *nix users have moved to SSH and OpenSSH and encourage Windows users to use PuTTY). If you just look to Linux for good packages, you'll miss a lot of GREAT stuff -- which may even be in your distro's repository already. There is NO reason for a special Internet Browser for Linux.