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Arnold Schwarzenegger tweets that son is improving

(CBS/AP) Former California Gov. Arnold Schwarzenegger says his son's condition is improving after a body-boarding accident at a Malibu beach.

Pictures: Arnold Schwarzenegger
Pictures: Maria Shriver

His 13-year-old son, Christopher, was initially admitted to the intensive care unit and listed in serious condition July 17, after being hit by a large wave at the beach. He suffered a collapsed lung, broken bones and broken ribs.

"Thanks for all your support for Christopher," Schwarzenegger wrote Monday in a Twitter post. "It means a lot to me & to him. He's doing much better & we'll have him back at full speed soon.''

The boy's mother, Maria Shriver, has reporteldy been staying with him at the hospital; Schwarzenegger has been a frequent visitor.

Christopher is the youngest of the couple's four children. They are also parents to Katherine, 21, Christina, 20, and Patrick, 17.

Shriver filed for divorce from Schwarzenegger earlier this month, following the couple's separation after revelations that the former California governor fathered a child out of wedlock.