LOS ANGELES -?Former California Governor Arnold Schwarzenegger confirmed Monday that his 13-year-old son, who has been hospitalized since a boogie-boarding accident last week, was recovering.

"Thanks for all your support for Christopher," 63-year-old Schwarzenegger wrote on his Twitter account. "It means a lot to me and to him. He's doing much better, and we'll have him back at full speed soon."

Christopher Schwarzenegger,the youngest son of the former governor and California's First Lady Maria Shriver, has been in intensive care after he had suffered multiple broken bones and a collapsed lung as he took a bad spill off a boogie board in Malibu on July 17.

The estranged couple said in a joint statement issued last week that Christopher "is surrounded by his family and friends. He is a brave boy and is expected to make a full recovery."

The former governor has fathered a son out of wedlock 14 years ago with his long-time housekeeper. Shriver filed for divorce from her husband on July 1 after Schwarzenegger confirmed the affair.

A couple of more than 25 years, Schwarzenegger and Shriver have raised four children.