Kate Middleton 'Doing Well' After 'Successful' Abdominal Surgery, Palace Sources Say

While the Princess of Wales is doing well following her procedure, her road to recovery is just beginning

Kate Middleton is said to be “doing well” after undergoing abdominal surgery on Tuesday, palace sources tell PEOPLE.

On Thursday, Prince William, 41, paid a visit to his wife at the private London Clinic, where she is receiving treatment following her procedure. Kensington Palace said the surgery was "successful." PEOPLE understands that Kate’s issue is non-cancerous and William has shifted his schedule to support his wife and their three children — Prince George, 10, Princess Charlotte, 8, and Prince Louis, 5 — at home in Windsor.

While the royal is doing well following her procedure, her road to recovery is just beginning as she is expected to remain in the hospital for up to fourteen days and then continue her recuperation at home for around three months. In the meantime, Kate has canceled or postponed royal duties and planned foreign visits.

The first few months of the year were set to be busy ones for the Princess of Wales. Her early years initiative was at the center of her plans and Kate was expecting to undertake several engagements focused on the program. Indeed, her foundation held a meeting at Kensington Palace on Tuesday as she underwent her surgery.

Related: Kate Middleton Wants to 'Maintain Normality' for George, Charlotte and Louis amid Hospitalization

Kate had also been "looking forward" to upcoming travel abroad, PEOPLE was previously told. She and William were planning a brief visit to a yet-to-be-confirmed country where the British military is serving. The couple was also expected to make a short official tour to Rome, Italy, in the spring.

With Kate postponing public duties until well after Easter, she is not expected to undertake royal engagements until the second week of April.

March typically holds two days of celebrations for Kate. The first of the month marks St. David’s Day, which is the national day for Wales. With her and William enthusiastic in their roles as the Prince and Princess of Wales, they have often marked that day with outings. Last year, Kate led the commemorations with the Welsh Guards at a barracks near Windsor.

And on St. Patrick’s Day, Kate usually takes part in the annual festivities alongside the Irish Guards. Kate was made honorary Colonel of the Irish Guards when regiments were reassigned shortly after Queen Elizabeth's death.

As President of the Rugby Football Union, which leads the sport in England (alongside William who represents the Welsh Rugby Union), the couple usually attends a game or two during the Six Nation tournament for their teams, which kicks off on February 3.

Princess Kate’s last official engagement was on Dec. 8 when she hosted her annual Christmas concert at Westminster Abbey. She was last seen publicly when she took part in the royal family's traditional walk to church on Christmas Day alongside William and their children.

In a statement on Wednesday, the palace said Kate "appreciates the interest" news of her surgery will generate, but she "hopes that the public will understand her desire to maintain as much normality for her children as possible; and her wish that her personal medical information remains private"

"Kensington Palace will, therefore, only provide updates on Her Royal Highness’ progress when there is significant new information to share," according to the statement.

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