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Global Smooth Solutions for the Inviscid SQG Equation

2020-09-28 Mathematics
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Release : 2020-09-28
Genre : Mathematics
Kind : eBook
Book Rating : 140/5 ( reviews)

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Book Synopsis Global Smooth Solutions for the Inviscid SQG Equation by : Angel Castro

Download or read book Global Smooth Solutions for the Inviscid SQG Equation written by Angel Castro. This book was released on 2020-09-28. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, the authors show the existence of the first non trivial family of classical global solutions of the inviscid surface quasi-geostrophic equation.

The 2D Compressible Euler Equations in Bounded Impermeable Domains with Corners

2021-06-21 Education
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Release : 2021-06-21
Genre : Education
Kind : eBook
Book Rating : 216/5 ( reviews)

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Book Synopsis The 2D Compressible Euler Equations in Bounded Impermeable Domains with Corners by : Paul Godin

Download or read book The 2D Compressible Euler Equations in Bounded Impermeable Domains with Corners written by Paul Godin. This book was released on 2021-06-21. Available in PDF, EPUB and Kindle. Book excerpt: We study 2D compressible Euler flows in bounded impermeable domains whose boundary is smooth except for corners. We assume that the angles of the corners are small enough. Then we obtain local (in time) existence of solutions which keep the L2 Sobolev regularity of their Cauchy data, provided the external forces are sufficiently regular and suitable compatibility conditions are satisfied. Such a result is well known when there is no corner. Our proof relies on the study of associated linear problems. We also show that our results are rather sharp: we construct counterexamples in which the smallness condition on the angles is not fulfilled and which display a loss of L2 Sobolev regularity with respect to the Cauchy data and the external forces.

Local Well-Posedness and Break-Down Criterion of the Incompressible Euler Equations with Free Boundary

2021-07-21 Education
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Release : 2021-07-21
Genre : Education
Kind : eBook
Book Rating : 898/5 ( reviews)

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Book Synopsis Local Well-Posedness and Break-Down Criterion of the Incompressible Euler Equations with Free Boundary by : Chao Wang

Download or read book Local Well-Posedness and Break-Down Criterion of the Incompressible Euler Equations with Free Boundary written by Chao Wang. This book was released on 2021-07-21. Available in PDF, EPUB and Kindle. Book excerpt: 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 +ε. 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.

Operator Theory on One-Sided Quaternion Linear Spaces: Intrinsic $S$-Functional Calculus and Spectral Operators

2021-02-10 Mathematics
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Release : 2021-02-10
Genre : Mathematics
Kind : eBook
Book Rating : 388/5 ( reviews)

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Book Synopsis Operator Theory on One-Sided Quaternion Linear Spaces: Intrinsic $S$-Functional Calculus and Spectral Operators by : Jonathan Gantner

Download or read book Operator Theory on One-Sided Quaternion Linear Spaces: Intrinsic $S$-Functional Calculus and Spectral Operators written by Jonathan Gantner. This book was released on 2021-02-10. Available in PDF, EPUB and Kindle. Book excerpt: Two major themes drive this article: identifying the minimal structure necessary to formulate quaternionic operator theory and revealing a deep relation between complex and quaternionic operator theory. The theory for quaternionic right linear operators is usually formulated under the assumption that there exists not only a right- but also a left-multiplication on the considered Banach space $V$. This has technical reasons, as the space of bounded operators on $V$ is otherwise not a quaternionic linear space. A right linear operator is however only associated with the right multiplication on the space and in certain settings, for instance on quaternionic Hilbert spaces, the left multiplication is not defined a priori, but must be chosen randomly. Spectral properties of an operator should hence be independent of the left multiplication on the space.

Łojasiewicz-Simon Gradient Inequalities for Coupled Yang-Mills Energy Functionals

2021-02-10 Mathematics
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Release : 2021-02-10
Genre : Mathematics
Kind : eBook
Book Rating : 023/5 ( reviews)

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Book Synopsis Łojasiewicz-Simon Gradient Inequalities for Coupled Yang-Mills Energy Functionals by : Paul M Feehan

Download or read book Łojasiewicz-Simon Gradient Inequalities for Coupled Yang-Mills Energy Functionals written by Paul M Feehan. This book was released on 2021-02-10. Available in PDF, EPUB and Kindle. Book excerpt: The authors' primary goal in this monograph is to prove Łojasiewicz-Simon gradient inequalities for coupled Yang-Mills energy functions using Sobolev spaces that impose minimal regularity requirements on pairs of connections and sections.

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