Regularity of solutions to characteristic boundary value problem for symmetric systems

Nishitani, Tatsuo; Takayama, Masahiro

doi:10.1007/978-1-4612-2014-5_14

Cited by 3 publications

(3 citation statements)

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“…We need to approximate the initial data by a sequence of smooth vector fields which belong to and are bounded in the same function spaces as u 0 , that is, in conormal spaces. Density results for conormal spaces are known, see for example [15,16]. However, these density results are false within the class of general divergence free vector fields.…”

Section: Approximation Procedures and End Of Proofsmentioning

confidence: 99%

“…However, these density results are false within the class of general divergence free vector fields. Indeed, it is proved in [15,16] that C ∞ 0 is dense in H m co . A similar density result cannot be true for divergence free vector fields because a divergence free vector field has a normal trace at the boundary.…”

Section: Approximation Procedures and End Of Proofsmentioning

confidence: 99%

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Uniform time of existence for the alpha Euler equations

Busuioc

Iftimie

Filho

et al. 2016

Journal of Functional Analysis

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Abstract. We consider the α-Euler equations on a bounded three-dimensional domain with frictionless Navier boundary conditions. Our main result is the existence of a strong solution on a positive time interval, uniform in α, for α sufficiently small. Combined with the convergence result in [4], this implies convergence of solutions of the α-Euler equations to solutions of the incompressible Euler equations when α → 0. In addition, we obtain a new result on local existence of strong solutions for the incompressible Euler equations on bounded three-dimensional domains. The proofs are based on new a priori estimates in conormal spaces.

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Section: Approximation Procedures and End Of Proofsmentioning

confidence: 99%

Section: Approximation Procedures and End Of Proofsmentioning

confidence: 99%

Uniform time of existence for the alpha Euler equations

Busuioc

Iftimie

Filho

et al. 2016

Journal of Functional Analysis

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“…In next section we write (1) as a symmetric hyperbolic system [4]; with our assumptions it becomes partly characteristic and partly noncharacteristic: more precisely, the boundary Γ 1 is noncharacteristic while the boundary Γ 0 is characteristic of rank two. To our knowledge no general theory is available for these problems even if some partial results may be found in [6,7,8,11,13].…”

Section: Introductionmentioning

confidence: 99%

Inflow-outflow problems for Euler equations in a rectangular cylinder

Gazzola¹,

Secchi²

2001

NoDEA, Nonlinear differ. equ. appl.

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We prove that some inflow-outflow problems for the Euler equations in a (nonsmooth) bounded cylinder admit a regular solution. The problems considered are symmetric hyperbolic systems with partly characteristic and partly noncharacteristic boundary; for such problems, no general theory is available. Therefore, we introduce particular spaces of functions satisfying suitable additional boundary conditions which allow to determine a regular solution by means of a ''reflection technique''.2000 Mathematics Subject Classification: 35L45, 76N10, 76J20.

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