The IRS will notify you by mail. According to the IRS instructions
for Form 8379 - Injured Spouse Allocation:
Generally, if you file Form 8379 with a joint
return on paper, the time needed to process it is about 14 weeks (11 weeks if
filed electronically). If you file Form 8379 by itself after a joint return has
been processed, the time needed is about 8 weeks.