The couple put on a united front at an awards ceremony earlier this week, rubbishing reports that they were heading for divorce.
A source told Now magazine that while they might have a turbulent romance, Katy has no plans to bail out.
“They have a stormy relationship, but she says they’re in it for the long haul,” said the insider.
Another claimed that Katy hadn’t been happy about having to fly to New York from Europe where she was touring to spend her wedding anniversary with Russell following a last-minute change of plan.
“They’d planned to meet in Ireland,” said the source.
“But then Russell agreed to some stand-up dates in LA. They compromised on New York but Katy was upset.”