Global Smooth Solutions for the Inviscid SQG Equation - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Global Smooth Solutions for the Inviscid SQG Equation write by Angel Castro. This book was released on 2020. Global Smooth Solutions for the Inviscid SQG Equation available in PDF, EPUB and Kindle. "In this memoir, we show the existence of the first non trivial family of classical global solutions of the inviscid surface quasi-geostrophic equation"--
Global Smooth Solutions for the Inviscid SQG Equation
Global Smooth Solutions for the Inviscid SQG Equation - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Global Smooth Solutions for the Inviscid SQG Equation write by Angel Castro. This book was released on 2020-09-28. Global Smooth Solutions for the Inviscid SQG Equation available in PDF, EPUB and Kindle. 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
The 2D Compressible Euler Equations in Bounded Impermeable Domains with Corners - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The 2D Compressible Euler Equations in Bounded Impermeable Domains with Corners write by Paul Godin. This book was released on 2021-06-21. The 2D Compressible Euler Equations in Bounded Impermeable Domains with Corners available in PDF, EPUB and Kindle. 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
Local Well-Posedness and Break-Down Criterion of the Incompressible Euler Equations with Free Boundary - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Local Well-Posedness and Break-Down Criterion of the Incompressible Euler Equations with Free Boundary write by Chao Wang. This book was released on 2021-07-21. Local Well-Posedness and Break-Down Criterion of the Incompressible Euler Equations with Free Boundary available in PDF, EPUB and Kindle. 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
Operator Theory on One-Sided Quaternion Linear Spaces: Intrinsic $S$-Functional Calculus and Spectral Operators - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Operator Theory on One-Sided Quaternion Linear Spaces: Intrinsic $S$-Functional Calculus and Spectral Operators write by Jonathan Gantner. This book was released on 2021-02-10. Operator Theory on One-Sided Quaternion Linear Spaces: Intrinsic $S$-Functional Calculus and Spectral Operators available in PDF, EPUB and Kindle. 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.
