Use null_value for a date field in Elasticsearch mapping

output.json

{
  "took" : 3,
  "timed_out" : false,
  "_shards" : {
    "total" : 1,
    "successful" : 1,
    "failed" : 0
  },
  "hits" : {
    "total" : 2,
    "max_score" : 1.0,
    "hits" : [ {
      "_index" : "test",
      "_type" : "doc",
      "_id" : "2",
      "_score" : 1.0,
      "_source":{
    "cards": "2",
    "last_updated": "2013-02-02 01:02:03"
}

    }, {
      "_index" : "test",
      "_type" : "doc",
      "_id" : "3",
      "_score" : 1.0,
      "_source":{
    "cards": "3",
    "last_updated": null
}

    } ]
  }
}

run.sh

#!/bin/bash

curl -XDLETE localhost:9200/test
echo
curl -XPUT localhost:9200/test -d '{
    "settings": {
        "index.number_of_shards": 1,
        "index.number_of_replicas": 0
    },
    "mappings": {
        "doc": {
            "_timestamp": {
                "enabled": "true"
            },
            "properties": {
                "cards": {
                    "type": "integer"
                },
                "last_updated": {
                    "type": "date",
                    "format": "yyyy-MM-dd HH:mm:ss",
					"null_value": "now"
                }
            }
        }
    }
}
'
curl -XPOST localhost:9200/test/doc/1 -d '{
    "cards": "1",
    "last_updated": "2012-01-01 12:13:14"
}
'
curl -XPOST localhost:9200/test/doc/2 -d '{
    "cards": "2",
    "last_updated": "2013-02-02 01:02:03"
}
'
curl -XPOST localhost:9200/test/doc/3 -d '{
    "cards": "3",
    "last_updated": null
}
'
curl -X POST 'http://localhost:9200/test/_refresh'
echo
curl -X GET 'http://localhost:9200/test/doc/_search?pretty' -d '{
    "query": {
        "filtered": {
            "query": {
                "match_all": {}
            },
            "filter": {
                "range": {
                    "last_updated": {
                        "gte": "2013-01-01 00:00:00"
                    }
                }
            }
        }
    }
}
'