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 . <EOS>