Is it possible to lift a ship sized vehicle into the sky by following modern day aerodynamics and aircraft design?
Possible: Yes 

You can in theory lift anything. To do this you will simply need to generate an equal or exceeding amount of lift than the weight of the object. You will also need to generate enough thrust to achieve said situation. The closest thing I can think of to this was Howard Hughes Spruce Goose which did actually fly. If you are talking about the kind of vertical hovering that the ship in the movie does you would need to generate an amazing amount of thrust to achieve that. A US Nimitz-Class aircraft carrier displaces 100,000 long tons (224,000,000 LBS) so you would need to generate at least that much thrust but in reality you would need to generate more to overcome drag and to actually accelerate the craft vertically. For a point of comparison the Saturn V rocket weighed 3270 tons (6,540,000 pounds).  

If we work through a quick example (these are very very lose numbers), lets take the Nimitz at 224,000,000LBS and the GE90 jet engine (currently the biggest turbo fan jet). The GE90 generates about 115,000 lbf of thrust. So it would take just under 2000 GE90s to generate enough thrust. But lets round it off at 2000 for ease of use and a bit of extra power. The diameter of the engine is 3.429m and the Nimitz is 332.8m long. You would need arms with 10 engines a piece just to make all 2000 engines fit down the length of the side. If they were stacked directly next to each other the arms would be about 35m in length. The bigger issue here is fuel flow/mass. You would need to lift enough fuel to actually power these engines for a useable amount of time. 

On the more sifi side of things, you could use the Nimitz's nuclear reactor to power ducted fans which overcomes the fuel problem to an extent but I dont have any numbers on that.