[BOT] update articles.json

data/articles.json

@@ -41,7 +41,7 @@
       "paperId": "de167c589a7a334f2046a1687c24d6f7fa74eb15",
       "url": "https://www.semanticscholar.org/paper/de167c589a7a334f2046a1687c24d6f7fa74eb15",
       "title": "On the instability of travelling wave solutions for the transport-Stokes equation",
-      "abstract": "In this paper, we investigate the instability of the spherical travelling wave solutions for the Transport-Stokes system in $\\mathbb{R}^3$. First, a classical scaling argument ensures instability among all probability measures for the Wasserstein metric and the $L^1$ norm. Secondly, we investigate the instability among patch solutions with a perturbed surface. To this end, we study the linearized system of a contour dynamics equation derived in [18] in the case where the support of the patch is axisymmetric and is described by spherical parametrization. We show numerically the existence of positive eigenvalues, which ensures the instability of the linearized system. Eventually we investigate numerically the instability of the travelling wave by solving the Transport-Stokes equation using a finite element method on FreeFem.",
+      "abstract": "In this paper, we investigate the instability of the spherical travelling wave solutions for the Transport-Stokes system in $\\mathbb{R}^3$. First, a classical scaling argument ensures instability among all probability measures for the Wasserstein metric and the $L^1$ norm. Secondly, we investigate the instability among patch solutions with a perturbed surface. To this end, we study the linearized system of a contour dynamics equation derived in [18] in the case where the support of the patch is axisymmetric and is described by spherical parametrization and show well-posedness of the linearized system. The actual version does not include the investigation of the eigenvalue and will be completed in the future. Eventually we investigate numerically the instability of the travelling wave by solving the Transport-Stokes equation using a finite element method on FreeFem.",
       "publicationDate": "2023-11-24",
       "authors": [
         {