Exact controllability of the Navier-Stokes and Boussinesq equations

Autor:	Andrei V. Fursikov, O. Yu. Imanuvilov
Rok vydání:	1999
Předmět:	Controllability General Mathematics Mathematical analysis Linear system Bibliography Navier stokes Boussinesq approximation (water waves) Mathematics
Zdroj:	Russian Mathematical Surveys. 54:565-618
ISSN:	1468-4829 0036-0279
DOI:	10.1070/rm1999v054n03abeh000153
Popis:	ContentsIntroduction § 1. Statement of the problem. Main results1.1. Exact boundary controllability of the Navier-Stokes equations1.2. Local exact distributed controllability of the Navier-Stokes equations1.3. Exact controllability of the Boussinesq system1.4. Exact local controllability and approximate controllability of the Boussinesq system1.5. Some applications § 2. Carleman estimates2.1. Preliminaries2.2. Carleman estimates for solutions of system (2.9), (2.10)2.3. Definitive estimates § 3. Solubility of the exact controllability problem for the linearized Boussinesq system3.1. Statement of the problem3.2. An auxiliary extremal problem3.3. Proof of the main result § 4. Local exact controllability of the Boussinesq system § 5. Approximate controllability of the Boussinesq system: reduction to a linear system of a special form5.1. The idea of the proof5.2. Approximate controllability of the Boussinesq system § 6. Exact controllability of a linear system6.1. Proof of Lemma 5.16.2. Proof of Theorem 5.1 Bibliography
Databáze:	OpenAIRE
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