Sending Email Using JQuery Ajax without Refresh

I'm having trouble trying to use this form submission method by email without refreshing the page. I still do not know much about Ajax, so I'm not sure if the code is correct, I even tried other methods, copying and pasting the code and only changing some things to see if it was going to, but I could not. The problem is that clicking the submit button does not take any action. The function is not called.

Js code:

$(function($) {

        $("#form1").submit(function() {

            var nome = $("#nome").val();
            var email = $("#email").val();
            var mensagem = $("#mensagem").val();

            $("#status").html("<img src='loader.gif'/>");

            $.post('email.php', {nome: nome, email: email, mensagem: mensagem }, function(envia) {

                    $("#status").slideDown();

                    if (envia != false) {

                        $("#status").html(envia);
                    } 

                    else {

                        $("#status").html("Mensagem enviada com sucesso!");

                        $("#nome").val("");
                        $("#email").val("");
                        $("#mensagem").val("");
                    }
            });
        });
       });

Form:

 <form id="form1" class="row" method="post" action="javascript:function()">
        <input type="text" placeholder="Nome:" class="form-control" name="nome"/>
        <input type="email" placeholder="E-mail:" class="form-control" name="email"/>
        <textarea placeholder="Mensagem:" class="form-control" name="mensagem"></textarea>
        <input type="submit" class="btn btn-default btn-link" name="submit">
</form>

PHP

<?php

require_once("class/class.phpmailer.php");
date_default_timezone_set('America/Sao_Paulo');
$ip = getenv("REMOTE_ADDR");

$mail = new PHPMailer(true);
$mail->SetLanguage("br");
// $mail->IsSMTP();
$mail->SMTPDebug = 0;   
$mail->SMTPAuth = true; 
$mail->SMTPSecure = 'ssl';

$nomeusuario = utf8_decode($_POST['nome']);
$emailusuario = utf8_decode($_POST['email']);
$mensagem = utf8_decode($_POST['mensagem']);

$mail->Host = 'email-ssl.com.br';
$mail->SMTPAuth = true;
$mail->Port = 465;
$mail->Username = '';
$mail->Password = '';

$mail->From = $emailusuario;
$mail->FromName = $nomeusuario;
$mail->AddAddress('', '');
$mail->Subject = "";
$mail->AddBcc($emailusuario);
$mail->Body = $mensagem;

    if(!$mail->Send()) {
      echo "Mensagem de erro: " . $mail->ErrorInfo;
    } else {
      echo "Mensagem enviada!";
    }

?>

When I try to put onsubmit in the form, an error image appears