Schoolchildren in the vicinity are being allowed to leave schools to go home, according to local broadcaster WCAU.
The road leading to the town of Paulsboro has been reopened but a limited evacuation is still in force.
The Coast Guard told WCAU that there is no immediate threat.
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Rain will spread southeastwards through N. Ireland, Wales and England overnight.
The woman used her daughter's own Facebook page to live-stream the attack after the teenager posted provocative pictures online.
A senior employee at the organisation reportedly derided the three-year-old royal for being 'royal, rich' and "advantaged'.