12/04/2012 10:51 EST | Updated 02/03/2013 05:12 EST

Prince William visits pregnant Kate in hospital

Prince William visits his wife Kate today at a London hospital where the Duchess of Cambridge is being treated for acute morning sickness.

The Duke of Cambridge arrived in a green Land Rover and entered the private King Edward VII Hospital without speaking to the phalanx of media and cameras gathered across the street, the BBC reported. William had spent the day with his wife at the hospital on Monday.

In announcing the royal pregnancy on Monday, St. James Palace said the duchess would be in hospital for several days being treated for Hyperemesis gravidarum, or acute morning sickness, which requires supplementary hydration and nutrients.

There has been no confirmed information provided on when the baby is due. Several media reports have indicated that Kate was approaching the 12th week of her pregnancy.

Kate has remained quite active in recent weeks.

As late as Nov. 30, the Duchess of Cambridge was photographed playing field hockey during a visit to her former preparatory school, St. Andrew's, which she attended from 1986 to 1995, in Berkshire, southern England.

Kate's pregnancy comes after a 2011 decision by the leaders of Britain and 15 Commonwealth nations endorsing new rules that give girls equal status with boys in the order of succession.

Experts caution that laws to enact the change have not yet been passed, which could cause uncertainty if Kate gives birth to a girl.