A Boundary Value Problem for a Second-Order Singular by Larin A. A.

By Larin A. A.

Show description

Read or Download A Boundary Value Problem for a Second-Order Singular Elliptic Equation in a Sector on the Plane PDF

Similar mathematics books

The language of mathematics : making the invisible visible

"The nice booklet of nature," stated Galileo, "can be learn in simple terms through those that be aware of the language within which it was once written. And this language is arithmetic. " within the Language of arithmetic, award-winning writer Keith Devlin finds the very important position arithmetic performs in our everlasting quest to appreciate who we're and the area we are living in.

Springer-Handbuch der Mathematik IV: Begründet von I.N. Bronstein und K.A. Semendjaew Weitergeführt von G. Grosche, V. Ziegler und D. Ziegler Herausgegeben von E. Zeidler

Als mehrbändiges Nachschlagewerk ist das Springer-Handbuch der Mathematik in erster Linie für wissenschaftliche Bibliotheken, akademische Institutionen und Firmen sowie interessierte Individualkunden in Forschung und Lehre gedacht. Es ergänzt das einbändige themenumfassende Springer-Taschenbuch der Mathematik (ehemaliger Titel Teubner-Taschenbuch der Mathematik), das sich in seiner begrenzten Stoffauswahl  besonders an Studierende richtet.

Additional resources for A Boundary Value Problem for a Second-Order Singular Elliptic Equation in a Sector on the Plane

Example text

140) wa = ω s = 0, ∂v s gpa ∂v a ρs0 νvs = −¯ ρa νva ( ¯ )2 a = αv (v a − v s ), ∂z RT ∂p s a a s s S ∂T a a a gp 2 ∂T = −cp ρ¯ νT ( ¯ ) = αT (T a − T s ), cp ρ0 νT ∂z RT ∂z ∂q ∂S = = 0. ∂pa ∂z Weak formulation of the PEs For the sake of simplicity we restrict ourselves to a regional problem using the beta-plane approximation. 6The same equation appears in [24] with ρ¯a replaced by ρa . Replacing ρa by ρ¯a is a necessary simplification for the developments below. SOME MATHEMATICAL PROBLEMS IN GFD 14-1-04 43 The function spaces that we introduce are similar to those used for the ocean and the atmosphere; hence V = V1 × V2 × V3 , H = H1 × H2 × H3 , where Vi = Via × Vis , Hi = Hia × His , the spaces Via , Hia , Vis , His being exactly like those of the atmosphere and the ocean respectively.

The governing equations In Ma , the variable is U a = (v a , T a , q) and in Ms the variable is U s = (v s , T s , S); we set also U = {U a , U s } , or alternatively v = {v a , v s } , T = {T a , T s } . 29), introducing only a superscript s for w, p, ρ0 , Fv , FT , FS , Tr , Sr , as well as the eddy viscosity coefficients µv , νv , etc. 136), and the differential operators are changed accordingly. Boundary Conditions Except for Γi , the boundary conditions are the same as for the ocean and the atmosphere taken separately.

Proof. 1 for dimension three. 1 and prove by contradiction that t∗ = t1 . 57) lim sup ||U (t)|| = +∞. 57). The bounds for ||U (t)|| will be derived sequentially: we will show successively that uz , ux , are in L∞ (0, t0 ; L2 (M)) and L2 (0, t0 ; H 1 (M)) where ϕx = ∂ϕ/∂x and ϕz = ∂ϕ/∂z; then we will prove at once that v, T and S are in L∞ (0, t0 ; H 1 ) and L2 (0, t0 ; H 2 ). In fact we will give the proofs for uz , ux , T the other quantities being estimated in exactly the same way. For the sake of simplicity, we assume hereafter that g = (gv , gT ) = 0.

Download PDF sample

Rated 4.33 of 5 – based on 7 votes