Android - Making Webview DomStorage persistant after app closed

I'm facing a huge problem developing an Android app which use a Webview to display datas. The website i'm using in the webview use localStorage API of HTML 5.

To enable this feature i've set the webview setting like this :

webview.getSettings().setDomStorageEnabled(true);
webview.getSettings().setJavaScriptEnabled(true);

So the localStorage API works but when I close the app (and kill the process), localStorage is completly erased and when I reload it, all my datas are lost.

My question is simple : How to make DomStorage of a Webview persistant even when we close the app ?

Thank you for all you future answers.