Context: Gaps, cavities and rings in circumstellar disks are signposts of disk evolution and planet-disk interactions. We follow the recent suggestion that Herbig Ae/Be disks with a flared disk harbour a cavity, and investigate the disk around HD~97048. Aims: We aim to resolve the 34$pm$ 4 au central cavity predicted by Maaskant et al. (2013) and to investigate the structure of the disk. Methods: We image the disk around HD~97048 using ALMA at 0.85~mm and 2.94~mm, and ATCA (multiple frequencies) observations. Our observations also include the 12CO J=1-0, 12CO J=3-2 and HCO+ J=4-3 emission lines. Results: A central cavity in the disk around HD~97048 is resolved with a 40-46 au radius. Additional radial structure present in the surface brightness profile can be accounted for either by an opacity gap at ~90 au or by an extra emitting ring at ~150 au. The continuum emission tracing the dust in the disk is detected out to 355 au. The 12CO J=3-2 disk is detected 2.4 times farther out. The 12CO emission can be traced down to $approx$ 10 au scales. Non-Keplerian kinematics are detected inside the cavity via the HCO+ J=4-3 velocity map. The mm spectral index measured from ATCA observations suggests that grain growth has occurred in the HD~97048 disk. Finally, we resolve a highly inclined disk out to 150 au around the nearby 0.5~$M_{odot}$ binary ISO-ChaI 126. Conclusions: The data presented here reveal a cavity in the disk of HD 97048, and prominent radial structure in the surface brightness. The cavity size varies for different continuum frequencies and gas tracers. The gas inside the cavity follows non-Keplerian kinematics seen in HCO+ emission. The variable cavity size along with the kinematical signature suggests the presence of a substellar companion or massive planet inside the cavity.
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