Though there are many reasons for divorce, divorces usually fall into two categories: no-fault and at-fault. The legal distinctions between these can vary state to state, as can the necessary paperwork, filing fees, and logistics. But what happens if you want a divorce and you can’t locate your spouse?  You might be a candidate for “divorce by publication.” Though the laws that govern divorce by default vary from state to state, they generally require that the two spouses have been living apart for a minimum amount of time, and that your spouse cannot be located despite diligent efforts to find him/her.
 
Here’s How the Process Works:

The traditional method of initiating a divorce action requires your attorney to serve your spouse with the divorce action at your spouse’s last known address, or in hand if your spouse can be located elsewhere.   
But, if after you’ve made diligent efforts to locate your spouse and can’t find him/her, you can ask the court for an Order of Notice by Publication.
This means that you must run a notice of your intent to divorce your spouse in a newspaper near the area of the spouse’s last known whereabouts. Generally, you’ll run this “legal advertisement” for about three weeks and your spouse will be given time to respond to the final notice.
If they don’t respond?  You and your attorney may proceed to finalizing your divorce by default.
You can divorce your spouse even if you can’t find him/her and even without their participation in the divorce proceeding, so long as a Judge is satisfied that your spouse had notice of the divorce proceeding.  When your spouse is M.I.A., notice by publication may be your best option.
An affidavit of marshal service attesting to the publication having taken place, and a copy of the publicized notice will generally be required to be filed with the court in your state.  Some states also require you to file an Affidavit of Military Service stating your spouse is not in the military.

Even without your spouse’s participation in the divorce proceeding, the court can enter orders regarding the effective dissolution of the martial estate, including property division, division of assets and debts, and orders affecting children - custody, visitation, child support - among others.
Having a Rocket Lawyer On Call attorney assist you in pursuing a divorce by default will help you avoid some of the legal hurdles you may face.

source:- https://www.rocketlawyer.com/article/divorce-by-publication.rl