Yauch - also known as MCA - passed away on Friday (May 4) at the age of 47 after a long battle with cancer.
> Adam Yauch 1964-2012: Obituary
> Adam Yauch 1964-2012: Beastie Boys' five classic music videos - watch
Ad-Rock - real name Adam Horovitz - took to the band's blog to thank friends and family for their "love and support".
"As you can imagine, s**t is just fkd up right now (sic)," he wrote. "But I wanna say thank you to all our friends and family (which are kinda one in the same) for all the love and support.
"I'm glad to know that all the love that Yauch has put out into the world is coming right back at him. Thank you."
Yauch's death has been met with a host of tributes, including performances by Coldplay and Red Hot Chili Peppers.
Watch the video for 'Sabotage' by Beastie Boys below: