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[null,"1.","Record Nr.",null,"UNINA9910970827103321"]
[null,null,"Autore",null,"Wang Chao"]
[null,null,"Titolo",null,"Local Well-Posedness and Break-Down Criterion of the Incompressible Euler Equations with Free Boundary"]
[null,null,"Pubbl/distr/stampa",null,"Providence : , : American Mathematical Society, , 2021"]
[{"$nulls":4},"©2021"]
[null,null,"ISBN",null,"9781470465247"]
[{"$nulls":4},"1470465248"]
[null,null,"Edizione",null,"[1st ed.]"]
[null,null,"Descrizione fisica",null,"1 online resource (132 pages)"]
[null,null,"Collana",null,"Memoirs of the American Mathematical Society ; ; v.270"]
[null,null,"Disciplina",null,"532"]
[null,null,"Soggetti",null,"Fluid mechanics"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Nota di bibliografia","Includes bibliographical references."]
[null,null,"Nota di contenuto",null,"Cover -- Title page -- Chapter 1. Introduction -- 1.1. Presentation of the problem -- 1.2. Some known results -- 1.3. Main results -- 1.4. Main ideas -- Chapter 2. Tools of paradifferential operators -- 2.1. Paradifferential operators -- 2.2. Functional spaces -- 2.3. Symbolic calculus -- 2.4. Tame estimates in Sobolev space -- 2.5. Tame estimates in Chemin-Lerner spaces -- 2.6. Commutator estimates -- Chapter 3. Parabolic evolution equation -- Chapter 4. Elliptic estimates in a strip -- 4.1. Elliptic boundary problem -- 4.2. Flattening the boundary and paralinearization -- 4.3. Elliptic estimates in Sobolev space -- 4.4. Tame elliptic estimates -- 4.5. Elliptic estimates in Besov space -- 4.6. Interior   ^{1,  } estimate -- Chapter 5. Dirichlet-Neumann operator -- 5.1. Definition and paralinearization -- 5.2. Sobolev estimate of the remainder -- 5.3. Tame estimate of the remainder -- 5.4. Hölder estimate of the remainder -- Chapter 6. New formulation and paralinearization -- 6.1. New formulation -- 6.2. Paralinearization -- Chapter 7. Estimate of the pressure -- 7.1.   ² estimate of the pressure -- 7.2. Hölder estimate of the pressure -- 7.3. Sobolev estimate of the pressure -- 7.4. Estimate of -- Chapter 8. Estimate of the velocity -- 8.1. Sobolev estimate of the velocity -- 8.2. The estimate of the irrotational part -- 8.3. The estimate of the rotational part -- Chapter 9. Proof of break-down criterion -- 9.1. The   ¹ energy estimate -- 9.2. Energy estimate of the trace of the velocity and the free surface -- 9.3. Energy estimate of the vorticity -- 9.4. Nonlinear estimates -- 9.5. Energy functional -- 9.6. Proof of Theorem 1.3 -- Chapter 10. Iteration scheme -- 10.1. Strategy -- 10.2. Iteration "]
[{"$nulls":4},"scheme -- 10.3. Existence of iteration scheme -- Chapter 11. Uniform energy estimates -- 11.1. Set-up -- 11.2. Energy functional."]
[{"$nulls":4},"11.3. Estimate of the velocity -- 11.4. Estimate of the pressure -- 11.5. Estimates of the remainder of DN operator -- 11.6. Energy estimates -- 11.7. Nonlinear estimates -- 11.8. Completion of the uniform estimate -- Chapter 12. Cauchy sequence and the limit system -- 12.1. Set-up -- 12.2. Elliptic estimates with a parameter -- 12.3. Energy estimates -- 12.4. The limit system -- Chapter 13. From the limit system to the Euler equations -- Chapter 14. Proof of Theorem 1.1 -- 14.1. Construction of approximate smooth solution -- 14.2. Uniform estimates and existence -- 14.3. Uniqueness of the solution -- Acknowledgement -- Bibliography -- Back Cover."]
[null,null,null,"Sommario/riassunto","\"In this paper, we prove the local well-posedness of the free boundary problem for the incompressible Euler equations in low regularity Sobolev spaces, in which the velocity is a Lipschitz function and the free surface belongs to C 3 2+. Moreover, we also present a Beale-Kato-Majda type break-down criterion of smooth solution in terms of the mean curvature of the free surface, the gradient of the velocity and Taylor sign condition\"--"]