Declare font in math mode

Question

How I make the default font in math mode has nothing to do with \setmainfont{some font}.

Why is the character specified by \it Times New Roman and the others are Computer Modern?

Now I want to change \it font which in math mode to Computer Roman.

Code:

\documentclass{book}
\usepackage{fontspec}
\usepackage[T1]{fontenc}
\setmainfont{Times New Roman}
\begin{document}
${v}_v＝{\it v}_0$，$x＝{\textit v} _0t$\par

$v_x=v_0$
\end{document}

Patch Code:

\documentclass{book}
\usepackage[no-math]{fontspec}
\showoutput
\setmainfont{Times New Roman}
\RequirePackage{unicode-math}
\setmathfont{TeX Gyre Termes Math}
\setmathfont{XITSMath-Regular}
[
    Extension = .otf,
    BoldFont = XITSMath-Bold,
    range={"1D70B, "2605, "2ACB, "2AFD, "23DC}
]
\setmathfont{STIX Two Math}[range={"221A, "221B, "221C}]
\setmathfont{Times New Roman}[range={"03C0}]
\setmathfont{XITSMath-Regular}
[
Extension = .otf,
BoldFont = XITSMath-Bold,
range={"2A00-"2AFF}
]
\begin{document}

${v}_v＝\mathit{v}_0$，$x＝\textit{v} _0t$\par

$v_x=v_0$
\end{document}

Answer 1

Never use T1 encoding with lualatex or xelatex.

\documentclass{book}
\usepackage{fontspec}
\showoutput
\setmainfont{Times New Roman}
\begin{document}
${v}_v＝{\it v}_0$，$x＝{\textit v} _0t$\par

$v_x=v_0$
\end{document}

Here {v}_v use computer modern math italic

{\it v} which should be \mathit{v} uses Times Roman Italic

{\textit v} which should be \textit{v} uses Times Roman Italic

add [no-math] then all but textit use the cm math fonts.

\documentclass{book}
\usepackage[no-math]{fontspec}
\showoutput
\setmainfont{Times New Roman}
\begin{document}
${v}_v＝\mathit{v}_0$，$x＝\textit{v} _0t$\par

$v_x=v_0$
\end{document}

Note you are using ， U+ff0c FULLWIDTH COMMA which is not in most latin fonts, use a normal ascii , similarly use = not U+ff1d FULLWIDTH EQUALS SIGN

\documentclass{book}
\usepackage[no-math]{fontspec}
\showoutput
\setmainfont{Times New Roman}
\begin{document}


${v}_v=\mathit{v}_0$, $x=\textit{v} _0t$\par

$v_x=v_0$
\end{document}

---

Your edited question shows using Stix Two mostly, but wanting to revert to Computer Modern locally. Here I set up an lm math version which is the default cm-style math font used by unicode-math but here just loaded in lm version.

\documentclass{book}
\usepackage{unicode-math}
\showoutput
\setmainfont{Times New Roman}
\setmathfont{STIX Two Math}
\setmathfont[version=lm]{Latin Modern Math}
\begin{document}


${v}_v=\mathit{v}_0$, $x=\textit{v} _0t$\par

$v_x=v_0$

{\mathversion{lm}


${v}_v=\mathit{v}_0$, $x=\textit{v} _0t$\par

$v_x=v_0$

}

\end{document}