Just define this alias:
alias psgrep='ps aux | grep '
And then call it with:
or anything you want to find!
On Linux you're better of with pgrep which is less error prone and has many nifty options (like searching by user, too).
It is installed on all Linux distros I've seen so far, maybe even BSDs, but not on OS X.
you can brew install pgrep on OSX ;p
brew install pgrep
Also pgrep handles the grep process which always appears when grepping ps aux.
A version which discards grep processes and removes case sensitivity:
alias psg='ps aux | grep -v " grep " | grep -i'