A rotary system with at least one radial gas bearing, comprising: - a housing, - a shaft rotatable relative to the housing and - at least one bearing assembly which has a first region bearing the shaft and supports the shaft relative to the housing by a radial gas bearing in which a gas gap, in particular an air gap, is formed between the bearing assembly and the shaft, the first region including or being formed by a tubular radial bearing sleeve, the inside of which has a bearing surface within which the shaft is supported in a radial direction, wherein the bearing assembly further comprises a third region held by the housing or integrated on or in the housing, and a second region connecting the first region to the third region, the second region being more resilient than the first region at least due to its shape and/or due to a shape of the first region, characterized in that - the second region of the bearing assembly is formed by an inner section of a spacer flange to which the first region of the bearing assembly, in particular the radial bearing sleeve, is connected, - the inner section of the spacer flange has at least one spring element, the shaping of which makes the second region of the bearing assembly more elastic than the first region of the bearing assembly, - the spring element includes at least one spring section of the inner section of the spacer flange, wherein the spring section extends transversely to the radial direction and - the inner section of the spacer flange contains a sleeve-shaped section which is connected in at least one axial end region to an axial end region of the spring section. - a housing, - a shaft rotatable relative to the housing and - at least one bearing assembly which has a first region bearing the shaft and supports the shaft relative to the housing by a radial gas bearing in which a gas gap, in particular an air gap, is formed between the bearing assembly and the shaft, the first region including or being formed by a tubular radial bearing sleeve, the inside of which has a bearing surface within which the shaft is supported in a radial direction, wherein the bearing assembly further comprises a third region held by the housing or integrated on or in the housing, and a second region connecting the first region to the third region, the second region being more resilient than the first region at least due to its shape and/or due to a shape of the first region, characterized in that the first region including or being formed by a tubular radial bearing sleeve, the inside of which has a bearing surface within which the shaft is supported in a radial direction, wherein the bearing assembly further comprises a third region held by the housing or integrated on or in the housing, and a second region connecting the first region to the third region, the second region being more resilient than the first region at least due to its shape and/or due to a shape of the first region, characterized in that - the second region of the bearing assembly is formed by an inner section of a spacer flange to which the first region of the bearing assembly, in particular the radial bearing sleeve, is connected, - the inner section of the spacer flange has at least one spring element, the shaping of which makes the second region of the bearing assembly more elastic than the first region of the bearing assembly, - the spring element includes at least one spring section of the inner section of the spacer flange, wherein the spring section extends transversely to the radial direction and - the inner section of the spacer flange contains a sleeve-shaped section which is connected in at least one axial end region to an axial end region of the spring section.