A system (300; 300') for an engine (100; 100'), comprising: a fuel tank ; at least one pump configured to provide liquid fuel from the fuel tank to a nozzle (120a; 320a) of a combustion section (116; 116') of the engine (100; 100'); and a bearing assembly (200; 250; 320b) that includes: a first structure (12; 262); and a second structure (14; 264) that is movable relative to the first structure (12; 262); characterised in that : the bearing assembly (200; 250; 320b) includes a membrane (16; 276, 278) disposed between the first structure (12; 262) and the second structure (14; 264), wherein the membrane (16; 276, 278) includes a plurality of perforations that receive liquid fuel from the at least one pump and supply the received liquid fuel in a region between the membrane (16; 276, 278) and the second structure (14; 264); the at least one pump includes a first pump and a second pump , wherein the first pump is configured to provide liquid fuel from the fuel tank to the nozzle (120a; 320a) via a first channel , and wherein the second pump is configured to provide liquid fuel from the fuel tank to the bearing assembly (200; 250; 320b) via a second channel (330b-1); and a closed circuit is formed between the fuel tank and the bearing assembly and is configured to return the liquid fuel that is supplied via the channel (330b-1) to the fuel tank via a return channel (330b-2). a fuel tank ; at least one pump configured to provide liquid fuel from the fuel tank to a nozzle (120a; 320a) of a combustion section (116; 116') of the engine (100; 100'); and a bearing assembly (200; 250; 320b) that includes: a first structure (12; 262); and a second structure (14; 264) that is movable relative to the first structure (12; 262); a first structure (12; 262); and a second structure (14; 264) that is movable relative to the first structure (12; 262); characterised in that : the bearing assembly (200; 250; 320b) includes a membrane (16; 276, 278) disposed between the first structure (12; 262) and the second structure (14; 264), wherein the membrane (16; 276, 278) includes a plurality of perforations that receive liquid fuel from the at least one pump and supply the received liquid fuel in a region between the membrane (16; 276, 278) and the second structure (14; 264); the at least one pump includes a first pump and a second pump , wherein the first pump is configured to provide liquid fuel from the fuel tank to the nozzle (120a; 320a) via a first channel , and wherein the second pump is configured to provide liquid fuel from the fuel tank to the bearing assembly (200; 250; 320b) via a second channel (330b-1); and a closed circuit is formed between the fuel tank and the bearing assembly and is configured to return the liquid fuel that is supplied via the channel (330b-1) to the fuel tank via a return channel (330b-2). the bearing assembly (200; 250; 320b) includes a membrane (16; 276, 278) disposed between the first structure (12; 262) and the second structure (14; 264), wherein the membrane (16; 276, 278) includes a plurality of perforations that receive liquid fuel from the at least one pump and supply the received liquid fuel in a region between the membrane (16; 276, 278) and the second structure (14; 264); the at least one pump includes a first pump and a second pump , wherein the first pump is configured to provide liquid fuel from the fuel tank to the nozzle (120a; 320a) via a first channel , and wherein the second pump is configured to provide liquid fuel from the fuel tank to the bearing assembly (200; 250; 320b) via a second channel (330b-1); and a closed circuit is formed between the fuel tank and the bearing assembly and is configured to return the liquid fuel that is supplied via the channel (330b-1) to the fuel tank via a return channel (330b-2). <EOS>