Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
134 tokens/sec
GPT-4o
9 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Global regular motions for compressible barotropic viscous fluids. Stability (1508.06127v1)

Published 25 Aug 2015 in math.AP

Abstract: We consider viscous compressible barotropic motions in a bounded domain $\Omega \subset \mathbb{R}3$ with the Dirichlet boundary conditions for velocity. We assume the existence of some special sufficiently regular solutions $v_s$ (velocity), $\varrho_s$ (density) of the problem. By the special solutions we can choose spherically symmetric solutions. Let $v$, $\varrho$ be a~solution to our problem. Then we are looking for differences $u=v-v_s$, $\eta=\varrho-\varrho_s$. We prove existence of $u$, $\eta$ such that $u,\eta\in L_\infty(kT,(k+1)T;H2(\Omega))$, $u_t,\eta_t\in L_\infty(kT,(k+1)T;H1(\Omega))$, $u\in L_2(kT,(k+1)T;H3(\Omega))$, $u_t\in L_2(kT,(k+1)T;H2(\Omega))$, where $T>0$ is fixed and $k \in \mathbb{N} \cup {0 }$. Moreover, $u$, $\eta$ are sufficiently small in the above norms. This also means that stability of the special solutions $v_s$, $\varrho_s$ is proved. Finally, we proved existence of solutions such that $v=v_s+u$, $\varrho=\varrho_s+\eta$.

Summary

We haven't generated a summary for this paper yet.