2006In Search For Water On Mars Via Clues From Antarctica
First of all, headlines usually have faulty grammar due to omission of words, so one can not pay too much attention to the English in headlines.
But, if we are trying to correct the grammar in that headline, I definitely would say 'in search of water'.
If you add "a" or "the", I would only say 'in (a)(the) search for water'.
The choice between "a" and "the" is the same as in any other "a"/"the" situation. If there is only one search that fits the headline, use "the", otherwise use "a".
My question is: Could we replace the phrase 'in search for' in the headline with 'in search of'? What's the difference between the phrases of 'in search of, in search for, in a search for, in the search for'?
Student or Learner