Asymptotic stability and sharp decay rates to the linearly stratified Boussinesq equations in horizontally periodic strip domain
We consider an initial boundary value problem of the multi-dimensional Boussinesq equations in the absence of thermal diffusion with velocity damping or velocity diffusion under the stress free boundary condition in horizontally periodic strip domain. We prove the global-in-time existence of classic...
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| Veröffentlicht in: | Calculus of variations and partial differential equations 2023-06, Vol.62 (5), Article 141 |
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| creator | Jang, Juhi Kim, Junha |
| description | We consider an initial boundary value problem of the multi-dimensional Boussinesq equations in the absence of thermal diffusion with velocity damping or velocity diffusion under the stress free boundary condition in horizontally periodic strip domain. We prove the global-in-time existence of classical solutions in high order Sobolev spaces satisfying high order compatibility conditions around the linearly stratified equilibrium, the convergence of the temperature to the asymptotic profile, and sharp decay rates of the velocity field and temperature fluctuation in all intermediate norms based on spectral analysis combined with energy estimates. To the best of our knowledge, our results provide first sharp decay rates for the temperature fluctuation and the vertical velocity to the linearly stratified Boussinesq equations in all intermediate norms. |
| doi_str_mv | 10.1007/s00526-023-02474-x |
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We prove the global-in-time existence of classical solutions in high order Sobolev spaces satisfying high order compatibility conditions around the linearly stratified equilibrium, the convergence of the temperature to the asymptotic profile, and sharp decay rates of the velocity field and temperature fluctuation in all intermediate norms based on spectral analysis combined with energy estimates. To the best of our knowledge, our results provide first sharp decay rates for the temperature fluctuation and the vertical velocity to the linearly stratified Boussinesq equations in all intermediate norms.</description><identifier>ISSN: 0944-2669</identifier><identifier>EISSN: 1432-0835</identifier><identifier>DOI: 10.1007/s00526-023-02474-x</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Analysis ; Asymptotic properties ; Boundary conditions ; Boundary value problems ; Boussinesq equations ; Calculus of Variations and Optimal Control; Optimization ; Control ; Damping ; Decay rate ; Domains ; Free boundaries ; Mathematical analysis ; Mathematical and Computational Physics ; Mathematics ; Mathematics and Statistics ; Norms ; Sobolev space ; Spectrum analysis ; Strip ; Systems Theory ; Theoretical ; Thermal diffusion ; Velocity distribution</subject><ispartof>Calculus of variations and partial differential equations, 2023-06, Vol.62 (5), Article 141</ispartof><rights>The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023. 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Var</addtitle><description>We consider an initial boundary value problem of the multi-dimensional Boussinesq equations in the absence of thermal diffusion with velocity damping or velocity diffusion under the stress free boundary condition in horizontally periodic strip domain. We prove the global-in-time existence of classical solutions in high order Sobolev spaces satisfying high order compatibility conditions around the linearly stratified equilibrium, the convergence of the temperature to the asymptotic profile, and sharp decay rates of the velocity field and temperature fluctuation in all intermediate norms based on spectral analysis combined with energy estimates. To the best of our knowledge, our results provide first sharp decay rates for the temperature fluctuation and the vertical velocity to the linearly stratified Boussinesq equations in all intermediate norms.</description><subject>Analysis</subject><subject>Asymptotic properties</subject><subject>Boundary conditions</subject><subject>Boundary value problems</subject><subject>Boussinesq equations</subject><subject>Calculus of Variations and Optimal Control; Optimization</subject><subject>Control</subject><subject>Damping</subject><subject>Decay rate</subject><subject>Domains</subject><subject>Free boundaries</subject><subject>Mathematical analysis</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Norms</subject><subject>Sobolev space</subject><subject>Spectrum analysis</subject><subject>Strip</subject><subject>Systems Theory</subject><subject>Theoretical</subject><subject>Thermal diffusion</subject><subject>Velocity distribution</subject><issn>0944-2669</issn><issn>1432-0835</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9kEtLAzEUhYMoWKt_wFXA9ehNJvPIshZfUHCj65DO3NiU6WSapNBx5U83toI7F5cLh--cA4eQawa3DKC6CwAFLzPgeTpRiWx_QiZM5DyDOi9OyQSkEBkvS3lOLkJYA7Ci5mJCvmZh3AzRRdvQEPXSdjaOVPctDSvtB9pio0fqdcRAo6NxhbSzPWrfjYlPujUWW3rvdiEkPWwpbndJdX2gtqcr5-2n66PuEj-gt649FHmbot1G2_6SnBndBbz6_VPy_vjwNn_OFq9PL_PZImtyJmNWI4i6ZIXEMi8b1JK3jGkmRVktl0xzY0wphUaRQ9WiXDamMQicVQxMi1WbT8nNMXfwbrvDENXa7XyfKhWvoQLBCiETxY9U410IHo0avN1oPyoG6mdpdVxapaXVYWm1T6b8aAoJ7j_Q_0X_4_oGrEyFng</recordid><startdate>20230601</startdate><enddate>20230601</enddate><creator>Jang, Juhi</creator><creator>Kim, Junha</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>JQ2</scope><orcidid>https://orcid.org/0000-0002-5962-6353</orcidid></search><sort><creationdate>20230601</creationdate><title>Asymptotic stability and sharp decay rates to the linearly stratified Boussinesq equations in horizontally periodic strip domain</title><author>Jang, Juhi ; Kim, Junha</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-8e0486159e636cea92d11a19467bb1a2fff694ae4307de9bcfcfe021710fde7d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Analysis</topic><topic>Asymptotic properties</topic><topic>Boundary conditions</topic><topic>Boundary value problems</topic><topic>Boussinesq equations</topic><topic>Calculus of Variations and Optimal Control; Optimization</topic><topic>Control</topic><topic>Damping</topic><topic>Decay rate</topic><topic>Domains</topic><topic>Free boundaries</topic><topic>Mathematical analysis</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Norms</topic><topic>Sobolev space</topic><topic>Spectrum analysis</topic><topic>Strip</topic><topic>Systems Theory</topic><topic>Theoretical</topic><topic>Thermal diffusion</topic><topic>Velocity distribution</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Jang, Juhi</creatorcontrib><creatorcontrib>Kim, Junha</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Computer Science Collection</collection><jtitle>Calculus of variations and partial differential equations</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Jang, Juhi</au><au>Kim, Junha</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Asymptotic stability and sharp decay rates to the linearly stratified Boussinesq equations in horizontally periodic strip domain</atitle><jtitle>Calculus of variations and partial differential equations</jtitle><stitle>Calc. Var</stitle><date>2023-06-01</date><risdate>2023</risdate><volume>62</volume><issue>5</issue><artnum>141</artnum><issn>0944-2669</issn><eissn>1432-0835</eissn><abstract>We consider an initial boundary value problem of the multi-dimensional Boussinesq equations in the absence of thermal diffusion with velocity damping or velocity diffusion under the stress free boundary condition in horizontally periodic strip domain. We prove the global-in-time existence of classical solutions in high order Sobolev spaces satisfying high order compatibility conditions around the linearly stratified equilibrium, the convergence of the temperature to the asymptotic profile, and sharp decay rates of the velocity field and temperature fluctuation in all intermediate norms based on spectral analysis combined with energy estimates. 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| subjects | Analysis Asymptotic properties Boundary conditions Boundary value problems Boussinesq equations Calculus of Variations and Optimal Control Optimization Control Damping Decay rate Domains Free boundaries Mathematical analysis Mathematical and Computational Physics Mathematics Mathematics and Statistics Norms Sobolev space Spectrum analysis Strip Systems Theory Theoretical Thermal diffusion Velocity distribution |
| title | Asymptotic stability and sharp decay rates to the linearly stratified Boussinesq equations in horizontally periodic strip domain |
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