The former couple, whose divorce was finalised more than a year ago, both attended a private heading in the Central Family Court in London.
Judge Martin O'Dwyer, who is overseeing the evidence, placed limits on what can be reported about the litigation, but the pair are embroiled in a dispute over money and the case is listed under the name Appleton.
A ruling on what other details can be revealed is expected to be made in the near future.
The former Oasis singer, 42, split from the blonde beauty, 40, in 2013 after he fathered a love child with American journalist Liza Ghorbani and had an affair with his former manager Debbie Gwyther - who he now lives with.
The duo, who got married on Valentine's Day in 2008 and have son Gene, 14, were granted a decree nisi at a hearing in April 2014 after Nicole said the rocker ''admitted adultery to me prior to it becoming publicised in national newspapers.''
Liam endured another court battle with Liza, with whom he has two-year-old daughter Gemma, in New York City earlier this year over child support.
Corgan took to Instagram to confirm rumours of new Pumpkins material, saying the first songs could arrive as early as May.