Carnations (Dianthus sp.) can be grown hydroponically. For you to succeed, you must dissolve their mineral salt nutrients in the water.

Plants, must get N,P,K and absorbable minor elements from a well-prepared recipe of soluble salts dissolved in the water (the 'fertilizer solution') , probably with a moderate solution (EC about 2.2) strength with a composition sold commercially something like *hydroponic* tomatoes also use.

Thank you PupillaCharites..
Yes, it works :)
I went abroad these past ten days, and I put my carnation seedlings in a vase with its root touching water,
And it keeps living! :)
but it is so thin, maybe because of lack of nutrients like you say.
I'll add the NPk elements into it