Let $R$ be a regular local complete (with respect to the maximal ideal) ring with field of fraction $K$. Let $S\cong R[[x_1,\cdots, x_n]]/J$ (this is a Noetherian local ring which is an $R$-algebra).  
Is the completed tensor product (https://stacks.math.columbia.edu/tag/0AMU) 
 $S \widehat{\otimes}_R K$ a Noetherian local ring containing  $K$ ? 

Thoughts: Let $\mathfrak m$ be the unique maximal ideal of $S$. Since $K$ is a field, so the completed tensor product  $S \widehat{\otimes}_R K$  should just be the inverse limit of the system $\dfrac{S\otimes_R K}{\mathfrak m^n \otimes_R K}$. I have no idea how to analyze this.