Summary: We establish a Serrin-type regularity criterion in terms of pressure for Leray weak solutions to the Navier-Stokes equation in . It is known that if a Leray weak solution belongs to
then is regular. It is proved that if the pressure associated to a Leray weak solution belongs to
where is the critical Morrey-Campanato space (a definition is given in the text) for , then the weak solution is actually regular. Since this space is wider than and , the above regularity criterion is an improvement of Zhou’s result.