Simply use the delimiter ^$ to match the empty string, or use | to achieve the matching effect you want.

eg: Match mobile phone number, or empty

/^$|1[34578]\d{9}/

if(email && email.trim() && /^(\w)+(\.\w+)*@(\w)+((\.\w+)+)$/.test(email.trim())===false){
   // 填了邮箱并且邮箱不符合规则
}

//判断输入内容是否为空 
function IsNull(){ 
var str = document.getElementById('str').value.trim(); 
if(str.length==0){ 
alert('对不起，文本框不能为空或者为空格!');//请将“文本框”改成你需要验证的属性名称! 
} 
} 
function IsEmail() 
{ 
var str = document.getElementById('str').value.trim(); 
if(str.length!=0){ 
reg=/^\w+([-+.]\w+)*@\w+([-.]\w+)*\.\w+([-.]\w+)*$/; 
if(!reg.test(str)){ 
alert("对不起，您输入的字符串类型格式不正确!");//请将“字符串类型”要换成你要验证的那个属性名称！ 
} 
} 
}

/^(\w+(\.\w+)*@\w+(\.\w+)+|)$/

Among them, use /^...$/ to define the beginning and end, and there is a group in the middle. Pay attention to the vertical line at the end of the group. If nothing is written after the vertical line, it means it is empty.