Math & Science ⇒ text in a big system of equations

[nora_]

Hi everyone!
I am a relative new user of Latex. I must write a very big system of equations but, I would like to put some text at the beginning and at the end of the equation. Unfortunately, I am not able to do this.
Here you can find the code that I am using right now. The result is not satisfactory. Can you help me?
Kind regards,
Nora

Code: Select all

Find $\boldsymbol{u^+}\in \boldsymbol{H}^1(\Omega^+)$, $\boldsymbol{u^-}\in \boldsymbol{H}^1(\Omega^-)$, $p^+\in L^2(\Omega^+)$, $p^-\in L^2(\Omega^-)$, $\boldsymbol{\lambda_{in}^+}\in \boldsymbol{L}^2(\Gamma^+_{in})$, $\boldsymbol{\lambda_{in}^-}\in \boldsymbol{L}^2(\Gamma^-_{in})$, $\boldsymbol{\lambda_s^+}\in \boldsymbol{L}^2(\Gamma^+_s)$, $\boldsymbol{\lambda_s^-}\in \boldsymbol{L}^2(\Gamma^-_s)$, $\boldsymbol{\lambda_{sym}}\in \boldsymbol{L}^2(\Gamma_{sym})$ such that:
\begin{equation}
\left\{
\begin{aligned}
\label{eq:46}
&\int_{\Omega^+} \frac{\partial \boldsymbol{u^+}}{\partial t} \cdot \boldsymbol{v^+} + \int_{\Omega^-} \frac{\partial \boldsymbol{u^-}}{\partial t} \cdot \boldsymbol{v^-} + \int_{\Omega^+} [(\boldsymbol{u^+} \cdot \nabla) \boldsymbol{u^+}] \cdot \boldsymbol{v^+} + \int_\Omega [(\boldsymbol{u^-} \cdot \nabla) \boldsymbol{u^-}] \cdot \boldsymbol{v^-} \\& + \frac{1}{Re} \int_{\Omega^+} [(\nabla\boldsymbol{u^+} + \nabla\boldsymbol{u^+}^T)] \cdot \nabla\boldsymbol{v^+} + \frac{1}{Re} \int_{\Omega^-} [(\nabla\boldsymbol{u^-} + \nabla\boldsymbol{u^-}^T)] \cdot \nabla\boldsymbol{v^-}\\&- \int_{\Omega^+} \nabla p^+ \cdot \boldsymbol{v^+} - \int_{\Omega^-} \nabla p^- \cdot \boldsymbol{v^-} + \int_{\Gamma^+_{in}} \boldsymbol{\lambda^+_{in}}\cdot \boldsymbol{v^+} + \int_{\Gamma^-_{in}} \boldsymbol{\lambda^-_{in}}\cdot \boldsymbol{v^-} \\&+ \int_{\Gamma_s^+} \boldsymbol{\lambda_{s}^+}\cdot \boldsymbol{v^+} + \int_{\Gamma_s^-} \boldsymbol{\lambda_{s}^-}\cdot \boldsymbol{v^-} + \int_{\Gamma_{sym}} \boldsymbol{\lambda_{sym}}\cdot (\boldsymbol{v^+} - \boldsymbol{v^-})   = 0,\\
&-\int_{\Omega^+} q^+ \nabla \cdot \boldsymbol{u^+}-\int_{\Omega^-} q^- \nabla \cdot \boldsymbol{u^-} = 0,\\
&\int_{\Gamma^+_{in}}\boldsymbol{u^+}\cdot \boldsymbol{\mu^+} = \int_{\Gamma^+_{in}}\boldsymbol{u^+_{in}}\cdot \boldsymbol{\mu^+}, 
\quad \int_{\Gamma^-_{in}}\boldsymbol{u^-}\cdot \boldsymbol{\mu^-} = \int_{\Gamma^-_{in}}\boldsymbol{u^-_{in}}\cdot \boldsymbol{\mu^-},\\
&\int_{\Gamma^+_s} \boldsymbol{u^+} \cdot \boldsymbol{\eta^+} = \int_{\Gamma^+_s} \boldsymbol{u^+_s} \cdot \boldsymbol{\eta^+}, \quad \int_{\Gamma^-_s} \boldsymbol{u^-} \cdot \boldsymbol{\eta^-} = \int_{\Gamma^-_s} \boldsymbol{u^-_s} \cdot \boldsymbol{\eta^-},\\
&\int_{\Gamma_{sym}} (\boldsymbol{u^+} - \boldsymbol{u^-})\cdot\boldsymbol{\xi} = 0.
\end{aligned}
\right.
\end{equation}$\forall$ $\boldsymbol{v^+}\in \boldsymbol{H}^1(\Omega^+)$, $\boldsymbol{v^-}\in \boldsymbol{H}^1(\Omega^-)$, $q^+\in L^2(\Omega^+)$, $q^-\in L^2(\Omega^-)$, $\boldsymbol{\mu^+}\in \boldsymbol{L}^2(\Gamma^+_{in})$,  $\boldsymbol{\eta^+}\in \boldsymbol{L}^2(\Gamma^+_s)$, $\boldsymbol{\eta^-}\in \boldsymbol{L}^2(\Gamma^-_s)$, $\boldsymbol{\xi}\in \boldsymbol{L}^2(\Gamma_{sym})$.

[Stefan Kottwitz]

Hi Nora,

welcome to the forum!

For longer equations, use displayed math, such as equation and align, as you did with the large equation system. I understand the problem is with the long math expressions in the first sentence. In that case, I would change it and definitely not put such many math expressions inline within normal text. That's not a well understandable sentence in any language: "Find ... <many, many formulas> ... such that:". It's not the best style for readers to encapsulate large math expressions within normal words. Instead, I would change the wording completely. Text is text, math is math, text may have small math snippets such as variables inside. For example:

Find values for the following variables:

...

They shall fulfill these restrictions:

...

Btw. I suggest:

• Use many spaces to make your code readable, so one can work with it, also yourself. Sometime you need to change or debug it, readable code makes it easier. Space doesn't matter in the later output of formulas.
• Define macros for symbols instead of writing \boldsymbol{v^+} etc. a lot of times.
• Next time it would be good if you would post a compilable document, so we can really test it. It can be as easy as adding

  Code: Select all

  \documentclass{article}
  \usepackage{amsmath}
  \begin{document}
  ...
  \end{document}

and in complex cases your actual preamble.

Stefan

[nora_]

Thank you, Stefan!
I appreciate your suggestions. I'll try with displaymath.
Kind regards,
Nora