Your html5 jQuery application will work with the following browsers.

jQuery Mobile 1.0.1 Supported Platforms
jQuery Mobile has broad support for the vast majority of all modern desktop, smartphone, tablet, and e-reader platforms. In addition, feature phones and older browsers are supported because of our progressive enhancement approach. We’re very proud of our commitment to universal accessibility through our broad support for all popular platforms.

We use a 3-level graded platform support system: A (full), B (full minus Ajax), C (basic). The visual fidelity of the experience is highly dependent on the CSS rendering capabilities of the device and platform so not all A grade experience will be pixel-perfect but that’s the nature of the web.

A-grade – Full enhanced experience with Ajax-based animated page transitions.

Apple iOS 3.2-5.0 - Tested on the original iPad (4.3 / 5.0), iPad 2 (4.3), original iPhone (3.1), iPhone 3 (3.2), 3GS (4.3), 4 (4.3 / 5.0), and 4S (5.0)
Android 2.1-2.3 – Tested on the HTC Incredible (2.2), original Droid (2.2), HTC Aria (2.1), Google Nexus S (2.3). Functional on 1.5 & 1.6 but performance may be sluggish, tested on Google G1 (1.5)
Android 3.1 (Honeycomb)  – Tested on the Samsung Galaxy Tab 10.1 and Motorola XOOM
Android 4.0 (ICS)  – Since it’s very new, we don’t have a test phone in our lab but early reports are positive. Note: transitions can be poor on upgraded devices
Windows Phone 7-7.5 – Tested on the HTC Surround (7.0) HTC Trophy (7.5), LG-E900 (7.5), Nokia Lumia 800
Blackberry 6.0 – Tested on the Torch 9800 and Style 9670
Blackberry 7 – Tested on BlackBerry® Torch 9810
Blackberry Playbook (1.0-2.0) – Tested on PlayBook
Palm WebOS (1.4-2.0) – Tested on the Palm Pixi (1.4), Pre (1.4), Pre 2 (2.0)
Palm WebOS 3.0 – Tested on HP TouchPad
Firebox Mobile (10 Beta) – Tested on Android 2.3 device
Skyfire 4.1 - Tested on Android 2.3 device
Opera Mobile 11.5: Tested on Android 2.3
Meego 1.2 – Tested on Nokia 950 and N9
Samsung bada 2.0 – Tested on a Samsung Wave 3, Dolphin browser
UC Browser – Tested on Android 2.3 device
Kindle 3 and Fire - Tested on the built-in WebKit browser for each
Nook Color 1.4.1 – Tested on original Nook Color, not Nook Tablet
Chrome Desktop 11-17 - Tested on OS X 10.6.7 and Windows 7
Firefox Desktop 4-9 – Tested on OS X 10.6.7 and Windows 7
Internet Explorer 7-9 – Tested on Windows XP, Vista and 7
Opera Desktop 10-11 - Tested on OS X 10.6.7 and Windows 7
B-grade – Enhanced experience except without Ajax navigation features.
Blackberry 5.0: Tested on the Storm 2 9550, Bold 9770
Opera Mini (5.0-6.5) - Tested on iOS 3.2/4.3 and Android 2.3
Nokia Symbian^3 – Tested on Nokia N8 (Symbian^3), C7 (Symbian^3), also works on N97 (Symbian^1)
C-grade – Basic, non-enhanced HTML experience that is still functional
Blackberry 4.x - Tested on the Curve 8330
Windows Mobile - Tested on the HTC Leo (WinMo 5.2)
All older smartphone platforms and featurephones – Any device that doesn’t support media queries will receive the basic, C grade experience

TBL Specializes in jQuery Mobile: Touch-Optimized Web Framework for Smartphones & Tablets

A unified, HTML5-based user interface system for all popular mobile device platforms, built on the rock-solid jQuery and jQuery UI foundation. Its lightweight code is built with progressive enhancement, and has a flexible, easily themeable design.

jQuery mobile framework takes the “write less, do more” mantra to the next level: Instead of writing unique apps for each mobile device or OS, the jQuery mobile framework allows you to design a single highly-branded web site or application that will work on all popular smartphone, tablet, and desktop platforms.

A handy resource we like to use to keep updated on HTML5 is:

http://html5test.com/results-mobile.html

This site scores the major mobile browsers on HTML5 capaibilities. If you point your browser to http://html5test.com it will score your browser and give you a breakdown of your browser’s capabilities.