Matthew Bellamy and Kate Hudson
03/23/2014 at 03:00 PM EDT
Making it work?
Despite going through a recent rough patch in their relationship, Kate Hudson
, 34, and Matthew Bellamy
, 35, were spotted out together in Los Angeles on Friday looking relaxed and happy.
The couple – who got engaged
in 2011, and have a son
, Bingham, 2½ – had "been on the rocks for some time," a source close to the actress told PEOPLE
She also attended several events earlier this year without her 9-carat engagement ring.
Although Hudson – who also has a son
Ryder, 10, with ex-husband Chris Robinson of the Black Crowes – said in January
that she wasn't planning a wedding "anytime soon," the source said she was working to save her relationship with the Muse rocker.
"Kate is not giving up," the source told PEOPLE.
And so it seems!