wordpress action form doesn't work

I have a page-contact.php (i have my custom form)

            <form id="contact-form" name="contact-form" method="post" action="">
                <input type="text" name="name" placeholder="name"/>
                <input type="text" name="email" placeholder="email"/>
                <textarea rows="4" cols="50" name="message" 
                placeholder="message"> </textarea>
                <input id="submit" type="submit" name="submit" value="send"/>
            </form>

I have a my email_process.php (

<?php

$to        = 'info@domain.com';
$subject   = $_POST['name'];
$email     = $_POST['email'];
$body      = $_POST['message'];
$headers   = 'From: '.$email;
$mailCheck = mail($to, $subject, $body, $headers);

if($mailCheck) echo 1;

?>

I have also a js file for echo my success message and error message. The js form seems to work. but email_process.php is not working. For hand coded html without wordpress, the form action work "email_process.php" I think wordpress handle the code different. Can someone help me with this?

$(document).ready(function(){
    alertAnswer();
});


var check = 1;

function alertAnswer(){
$('#contact-form').submit(function(event){
    event.preventDefault();

    checkFormFill();
    if(check == false) alert("you didn't answer my form");
    else sendMessage();
});
}

function checkFormFill() {
check = 1;
$('#contact-form input[type="text"]').each(function(){
    if($(this).val().length < 3) check = false 
}) 

if($('#contact-form textarea').val().length < 3) check = false 
}

function eraseFormData() {
$('#contact-form input[type="text"]').each(function(){
    $(this).val('');
}) 

$('#contact-form textarea').val(''); 
}

function sendMessage() {
$.post('email_process.php',
    {
        name: $('input[name="name"]').val(),
        email: $('input[name="email"]').val(),
        message: $('textarea[name="message"]').val()
    },
    function(data) {
    if(data == 1) {
        $('#sendMessage').text("Thanks for contacting us. 
        We\'ll get back to you     shortly.");
        $('#sendMessage').css("margin-top","15px"); 
        eraseFormData(); 
    } 
    else $('#sendMessage').text("Sorry, an error occured. 
    Please try again!");
});
}