Solving browser compatibility issues in your Vue.js application involves addressing differences between different versions of popular browsers. Here's a general approach:

1. Install Cross-Browser Testing Tools: Use tools such as BrowserStack, Selenium, or similar to test your app on multiple browsers. This will help you identify compatibility issues early.

2. Use Feature Detection: Instead of using prefixes and polyfills for older browser versions, use feature detection. Modernizr is a good tool to detect which features are supported by the browser being used. You can then conditionally import or load polyfills only when necessary.

if (!Modernizr.fetch) {
  import 'whatwg-fetch';
}

3. Update Modern Browsers Only: Target modern browsers only in your build process and serve them compressed, minified code. This reduces the loading time for older browsers.

4. Polyfill Older Browser Features: Use polyfills to provide support for features that are not supported by older browsers. For example, use core-js or babel-polyfill to add Promise and other modern ES6 features.

5. Use a Compatibility Build of Vue: Instead of using the full build of Vue, use one of its compatibility builds that provides better browser support. These versions are compatible with older browsers without polyfills.

npm install vue@2.x --save

6. Optimize Bundle Size: Minify and gzip your JavaScript bundle to reduce the size of files sent over the network. This will help improve loading times for users on slower connections or older devices.

7. Provide Fallback Content: For critical features that might not be supported in older browsers, provide fallback content such as a message instructing users to update their browser or use an alternative feature.

Remember, Vue is designed to work well with modern web technologies and is not explicitly compatible with older versions of browsers. If compatibility issues arise, it's often best to upgrade the browsers your users are using, rather than trying to address them on a case-by-case basis.