After a busy fall in theaters, Carey Mulligan looks to keep herself occupied in 2012, landing the female lead in Coen Brothers next pic “Inside Llewyn Davis” and entering negotiations for a lead role in an untitled project for Spike Jonze.On “Inside Llewyn Davis,” Mulligan will star opposite Oscar Isaac in the Scott Rudin-produced pic that the Coens are writing, directing and producing with Scott Rudin. Story follows a musician who tries to make it in the New York music scene in the 1960s. StudioCanal is set to co-finance without a domestic distribution partner. Robert Graf will exec produce, while StudioCanal will handle international sales and distribute the film in France. It’s not known wether Mulligan will be called upon to sing — but she’s certainly shown vocal chops with several strong performances in “Shame.” For the Spike Jonze project, about world leaders uniting to discuss cataclysmic events, Mulligan would join Joaquin Phoenix with Charlie Kaufman penning the script. Megan Ellison is producing through her Annapurna Pictures. Mulligan is currently shooting “The Great Gatsby” for Warner Bros.; the plan is to jump into “Inside Llewyn Davis” in February, with the Spike Jonze pic in spring. Mulligan, repped by CAA and Julian Belfrage and Associates, has stayed busy on the indie circuit this fall, with turns in both Fox Searchlight’s “Shame” and FilmDistrict’s “Drive” (which also stars Isaac).