I am already using rtsp protocol to stream video on windows application and Silver-light web application. I have built rtsp server using Live555 lib
You can do this in 3 ways:
Write a plug in for live555 server which converts RTSP stream into RTMP. Then stream RTMP to web browser. From web browser using Flash player open RTMP stream.
Use third party server (e.g. wowza) which take RTSP stream from live555 as a input and stream out as RTMP. From web browser using Flash player open RTMP stream.
Recently live555 developer has added webrtc streaming in library. You can use this feature for web browser streaming. live555-webrtc-demo. This feature stream direct to web browser. But you need webrtc compatible web browser (e.g. firefox, chrome, opera).
I personally used second option as a web browser streaming solution.
I hope this will help you.